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SIEMENSSIEMENSSIEMENS

NX Nastran 11Verification Manual

Contents

Proprietary & Restricted Rights Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Overview of the Verification Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1Running the Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Linear Statics Verification Using Theoretical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Overview of Linear Statics Verification Using Theoretical Solutions . . . . . . . . . . . . . . . . . . . . 2-1Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1Understanding Comparisons with Theoretical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 2-2References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Point Load on a Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3Axial Distributed Load on a Linear Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4Distributed Loads on a Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6Moment Load on a Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7Edge Pressure on Beam Element - Torque Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9Thermal Strain, Displacement, and Stress on Heated Beam . . . . . . . . . . . . . . . . . . . . . 2-11Uniformly Distributed Load on Linear Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13Membrane Loads on a Linear Quadrilateral Thin Shell Element . . . . . . . . . . . . . . . . . . . 2-14Axial Loading on Rod Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16Stress on a Beam as It Expands and Closes a Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18Thin Wall Cylinder in Pure Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19Thin-walled Cantilever Beam in Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21Strain Energy of a Truss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23

Linear Statics Verification Using Standard NAFEMS Benchmarks . . . . . . . . . . . . . . . . . . 3-1

Overview of Linear Statics Verification Using Standard NAFEMS Benchmarks . . . . . . . . . . . . . 3-1Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Elliptic Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Cylindrical Shell Patch Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6Hemisphere-Point Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9Z-Section Cantilever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11Skew Plate Normal Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13Thick Plate Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15Solid Cylinder/Taper/Sphere — Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19

Normal Mode Dynamics Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

Overview of Normal Mode Dynamics Verification Using Theoretical Solutions . . . . . . . . . . . . . 4-1

NX Nastran 11 Verification Manual 3

Contents

Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1Understanding Comparisons with Theoretical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 4-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2Undamped Free Vibration — Single Degree of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . 4-2Two Degrees of Freedom Undamped Free Vibration — Principle Modes . . . . . . . . . . . . . . 4-4Three Degrees of Freedom Torsional System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6Two Degrees of Freedom Vehicle Suspension System . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8Two Degrees of Freedom Vehicle Suspension System . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9Cantilever Beam Undamped Free Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11Natural Frequency of a Cantilevered Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13

Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks . . . . . . . . . . . 5-1

Overview of Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks . . . . . 5-1Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

Beam Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2Pin-ended Cross — In-plane Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2Pin-ended Double Cross - In-plane Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4Free Square Frame - In-plane Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7Cantilever with Off-center Point Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9Deep Simply-Supported Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10Circular Ring — In-plane and Out-of-plane Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12Cantilevered Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

Shell Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16Thin Square Cantilevered Plate — Symmetric Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16Thin Square Cantilevered Plate — Anti-symmetric Modes . . . . . . . . . . . . . . . . . . . . . . . 5-19Free Thin Square Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-22Simply Supported Thin Square Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-24Simply Supported Thin Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-26Clamped Thin Rhombic Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-28Cantilevered Thin Square Plate with Distorted Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . 5-31Simply Supported Thick Square Plate, Test A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-35Simply Supported Thick Square Plate, Test B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-37Clamped Thick Rhombic Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-40Simply Supported Thick Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-43Cantilevered Square Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-46Cantilevered Tapered Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-48Free Annular Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-51Cantilevered Thin Square Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-54

Axisymmetric Solid and Solid Element Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-57Free Cylinder — Axisymmetric Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-57Thick Hollow Sphere — Uniform Radial Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59Simply Supported Annular Plate — Axisymmetric Vibration . . . . . . . . . . . . . . . . . . . . . . 5-62Deep Simply Supported "Solid" Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-65Simply Supported "Solid" Square Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-69Simply Supported "Solid" Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-72Cantilevered Solid Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-76

4 NX Nastran 11 Verification Manual

Contents

Contents

Verification Test Cases from the Societe Francaise des Mecaniciens . . . . . . . . . . . . . . . . 6-1

Overview of Verification Test Cases Provided by the Societe Francaise des Mecaniciens . . . . . 6-1Understanding the Test Case Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements . . . . . . . . . . . . . 6-2Short Beam on Two Articulated Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2Clamped Beams Linked by a Rigid Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3Transverse Bending of a Curved Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5Plane Bending Load on a Thin Arch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8Grid Point Load on an Articulated CONROD Truss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-10Articulated Plane Truss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-13Beam on an Elastic Foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-16

Mechanical Structures — Linear Statics Analysis with Shell Elements . . . . . . . . . . . . . . . . . 6-19Plane Shear and Bending Load on a Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19Infinite Plate with a Circular Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-21Uniformly Distributed Load on a Circular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24Torque Loading on a Square Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26Cylindrical Shell with Internal Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-28Uniform Axial Load on a Thin Wall Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-32Hydrostatic Pressure on a Thin Wall Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-35Pinched Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-38Spherical Shell with a Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-40Bending Load on a Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-43Uniformly Distributed Load on a Simply-Supported Rectangular Plate . . . . . . . . . . . . . . . 6-46Uniformly Distributed Load on a Simply-Supported Rhomboid Plate . . . . . . . . . . . . . . . . 6-49Shear Loading on a Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-52

Mechanical Structures — Linear Statics Analysis with Solid Elements . . . . . . . . . . . . . . . . . 6-54Solid Cylinder in Pure Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-54Internal Pressure on a Thick-Walled Spherical Container . . . . . . . . . . . . . . . . . . . . . . . 6-60Internal Pressure on a Thick-Walled Infinite Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . 6-65Prismatic Rod in Pure Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-70Thick Plate Clamped at Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-74

Mechanical Structures — Normal Mode Dynamics Analysis . . . . . . . . . . . . . . . . . . . . . . . . 6-79Lumped Mass-Spring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-79Short Beam on Simple Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-82Axial Loading on a Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-85Cantilever Beam with a Variable Rectangular Section . . . . . . . . . . . . . . . . . . . . . . . . . . 6-87Thin Circular Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-89Thin Circular Ring Clamped at Two Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-92Vibration Modes of a Thin Pipe Elbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-95Cantilever Beam with Eccentric Lumped Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-98Thin Square Plate (Clamped or Free) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-101Simply-Supported Rectangular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-103Thin Ring Plate Clamped on a Hub . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-105Vane of a Compressor - Clamped-free Thin Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-108Bending of a Symmetric Truss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-111Hovgaard's Problem — Pipes with Flexible Elbows . . . . . . . . . . . . . . . . . . . . . . . . . . 6-114Rectangular Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-117

Mechanical Structures — Normal Mode Dynamics Analysis and Model Response . . . . . . . . 6-120


Contents

Contents

Transient Response of a Spring-Mass System with Acceleration Loading . . . . . . . . . . . 6-120Transient Response of a Clamped-free Post . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-123

Stationary Thermal Tests — Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-126Hollow Cylinder - Fixed Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-126Hollow Cylinder - Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-129Cylindrical Rod - Flux Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-131Hollow Cylinder with Two Materials - Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-133Wall-Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-136Wall-Fixed Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-138L-Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-140Orthotropic Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-142Hollow Sphere - Fixed Temperatures, Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-145Hollow Sphere with Two Materials - Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-148

Thermo-mechanical Tests — Linear Statics Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-152Orthotropic Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-152Thermal Gradient on a Thin Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-155Simply-Supported Arch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-158

Material Nonlinear (Plasticity) Verification Using Standard NAFEMS Benchmarks . . . . . . . 7-1

Overview of the Material Nonlinear (Plasticity) Verification Using NAFEMS Test Cases . . . . . . . 7-1Understanding the Verification Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2Plane Strain Elements - Perfect Plasticity Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2Plane Strain Elements - Isotropic Hardening Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-6Plane Stress Elements - Perfect Plasticity Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10Plane Stress Elements - Isotropic Hardening Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14Solid Element - Perfect Plasticity Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-18Solid Element - Isotropic Hardening Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-23

Geometric Nonlinear Verification Using Standard NAFEMS Benchmarks . . . . . . . . . . . . . 8-1

Overview of the Geometric Nonlinear Verification Using NAFEMS Test Cases . . . . . . . . . . . . . 8-1Understanding the Verification Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2Straight Cantilever with End Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2Straight Cantilever with Axial End Point Load - Brick Elements . . . . . . . . . . . . . . . . . . . . 8-6Straight Cantilever with Axial End Point Load - BEAM Elements . . . . . . . . . . . . . . . . . . 8-11Lee's Frame Buckling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-15Large Displacement Elastic Response of a Hinged Spherical Shell Under Uniform PressureLoading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-21Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-21

6 NX Nastran 11 Verification Manual

Contents

Proprietary & Restricted Rights Notice

© 2016 Siemens Product Lifecycle Management Software Inc. All Rights Reserved.

This software and related documentation are proprietary to Siemens Product Lifecycle ManagementSoftware Inc. Siemens and the Siemens logo are registered trademarks of Siemens AG. NX is atrademark or registered trademark of Siemens Product Lifecycle Management Software Inc. or itssubsidiaries in the United States and in other countries.

NASTRAN is a registered trademark of the National Aeronautics and Space Administration. NXNastran is an enhanced proprietary version developed and maintained by Siemens Product LifecycleManagement Software Inc.

MSC is a registered trademark of MSC.Software Corporation. MSC.Nastran and MSC.Patran aretrademarks of MSC.Software Corporation.

All other trademarks are the property of their respective owners.

TAUCS Copyright and License

TAUCS Version 2.0, November 29, 2001. Copyright (c) 2001, 2002, 2003 by Sivan Toledo, Tel-AvivUniversity, [email protected]. All Rights Reserved.

TAUCS License:

Your use or distribution of TAUCS or any derivative code implies that you agree to this License.

THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY EXPRESSED ORIMPLIED. ANY USE IS AT YOUR OWN RISK.

Permission is hereby granted to use or copy this program, provided that the Copyright, this License,and the Availability of the original version is retained on all copies. User documentation of any codethat uses this code or any derivative code must cite the Copyright, this License, the Availability note,and "Used by permission." If this code or any derivative code is accessible from within MATLAB, thentyping "help taucs" must cite the Copyright, and "type taucs" must also cite this License and theAvailability note. Permission to modify the code and to distribute modified code is granted, providedthe Copyright, this License, and the Availability note are retained, and a notice that the code wasmodified is included. This software is provided to you free of charge.

Availability (TAUCS)

As of version 2.1, we distribute the code in 4 formats: zip and tarred-gzipped (tgz), with or withoutbinaries for external libraries. The bundled external libraries should allow you to build the testprograms on Linux, Windows, and MacOS X without installing additional software. We recommendthat you download the full distributions, and then perhaps replace the bundled libraries by higherperformance ones (e.g., with a BLAS library that is specifically optimized for your machine). If youwant to conserve bandwidth and you want to install the required libraries yourself, download thelean distributions. The zip and tgz files are identical, except that on Linux, Unix, and MacOS,unpacking the tgz file ensures that the configure script is marked as executable (unpack with tarzxvpf), otherwise you will have to change its permissions manually.


Chapter 1: Introduction

1.1 Overview of the Verification ManualThis guide contains verification test cases for NX Nastran. These test cases verify the function ofthe different NX Nastran analysis types using theoretical and benchmark solutions from well-knownengineering test cases. Each test case contains test case data and information, such as element typeand material properties, results, and references.

The guide contains test cases for:

• Linear Statics verification using theoretical solutions

• Linear Statics verification using standard NAFEMS benchmarks

• Normal Mode Dynamics verification using theoretical solutions

• Normal Mode Dynamics verification using standard NAFEMS benchmarks

• Verification Test Cases from the Societe Francaise des Mecaniciens

• Material Nonlinear (Plasticity) verification using standard NAFEMS benchmarks (NX Nastranonly)

• Geometric Nonlinear verification using standard NAFEMS benchmarks

1.2 Running the Test CasesAll verification test cases are available as *.dat files and are included in the NX Nastran installationin the directory path install_dir/NXr/nast/demo.

The test cases are relatively simple, and most have closed-form theoretical solutions. Differencesbetween finite element and theoretical solutions are in most cases negligible. Some tests wouldrequire an infinite number of elements to achieve an exact solution. Elements are chosen to achievereasonable engineering accuracy with reasonable computing times.

Note

Actual results from NX Nastran may vary insignificantly from the results presented in thisdocument. This variation is generally due to different methods of performing real numberalgorithms on different systems.

NX Nastran 11 Verification Manual 1-1

Chapter 2: Linear Statics Verification UsingTheoretical Solutions

2.1 Overview of Linear Statics Verification Using TheoreticalSolutionsThe purpose of these linear statics test cases is to verify the function of the NX Nastran softwareusing theoretical solutions. The test cases are relatively simple in form and most of them haveclosed-form theoretical solutions.

The theoretical solutions shown in these examples are from well-known engineering texts. For eachtest case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic.

The finite element method is very flexible in the types of physical problems represented. Theverification tests provided are not exhaustive in exploring all possible problems, but representcommon types of applications.

This overview provides information on the following:

• Understanding the test case format

• Understanding comparisons with theoretical solutions

• References

Understanding the Test Case Format

Each test case is structured with the following information.

• Test case data and information:

o Physical and material properties

o Finite element modeling (modeling procedure or hints)

o Units

o Solution type

o Element type

o Boundary conditions (loads, restraints)

• Results

• References (text from which a closed-form or theoretical solution was taken)

In addition to these example problems, test cases from NAFEMS (National Agency for Finite ElementMethods and Standards, National Engineering Laboratory, Glasgow, U.K.) have been executed.


Chapter 2: Linear Statics Verification Using Theoretical Solutions

Results for these test cases can be found in the next section, Linear Statics Analysis VerificationUsing NAFEMS Standard Benchmarks.

Understanding Comparisons with Theoretical Solutions

While differences in finite element and theoretical results are, in most cases, negligible, some testswould require an infinite number of elements to achieve the exact solution. Elements are chosen toachieve reasonable engineering accuracy with reasonable computing times.

Results reported here are results which you can compare to the referenced theoretical solution.Other results available from the analyses are not reported here. Results for both theoretical and finiteelement solutions are carried out with the same significant digits of accuracy.

The closed-form theoretical solution may have restrictions, such as rigid connections, that do notexist in the real world. These limiting restrictions are not necessary for the finite element model, butare used for comparison purposes. Verification to real world problems is more difficult but should bedone when possible.

The actual results from the NX Nastran software may vary insignificantly from the results presented inthis document. This variation is due to different methods of performing real numerical arithmetic ondifferent systems. In addition, it is due to changes in element formulations which have been made toimprove results under certain circumstances.

References

The following references have been used in the Linear Statics Analysis verification problemspresented:

1. Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992.

2. Harris, C. O. Introduction to Stress Analysis. New York Macmillan1959.

3. Roark, R. and Young, W. Formulas for Stress and Strain, 5th Edition. New York: McGraw-HillBook Company, 1975.

4. Shigley, J. and Mitchel L. Mechanical Engineering Design, 4th Edition. New York: McGraw-HillBook Company, 1983.

5. Timoshenko, S. Strength of Materials, Part I, Elementary Theory and Problems. New YorK: VanNorstrand Reinhold Company, 1955.

2-2 NX Nastran 11 Verification Manual


Linear Statics Verification Using Theoretical Solutions

Test Cases

Point Load on a Cantilever Beam

Determine the deflection of a beam at the free end. Determine the stress at the midpoint of the beam.

Test Case Data and Information

Input Files

mstvl001.dat

Units

Inch

Model Geometry

Length = 480 in.

Cross Sectional Properties

• Area = 30 x 30 in.

• Iy = Iz = 67500 in.4




Material Properties

• E = 30E06 psi

Finite Element Modeling

Create four successive linear beam (CBAR) elements along the X axis.

Boundary Conditions

• Restraints

o Restrain the left end of the beam in all six degrees.

• Loads

o Set grid force to 50,000 lb in. the -Y direction.

Solution Type

SOL 101 — Linear Statics

Results

Result Bench Value NX NastranVon Mises Stress, grid point 1 (psi) 5333. 5333.Y Deflection, grid point 5 (in) 0.9102 0.9130

References

Beer and Johnston. Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p. 716.

Axial Distributed Load on a Linear Beam

Determine the stress, elongation and resultant force due to an axial loading along a linear beam

element.


Input Files

mstvl002.dat




Units

Inch

Model Geometry

• Length = 300 in.


• Area = 9 in.2

• square cross section (3 in. x 3 in.)

Material Properties

• E = 30E+6 psi


Create 30 beam element along the X axis, each 10 in. long.

Boundary Conditions

• Restraints

o Restrain one end of the beam in all six degrees.

• Loads

o Apply the axial force as an axial distributed load (force per unit length) of 1000 lb/in. to the 10in. long element furthest from the restrained end.

The boundary conditions are shown in the following figure:

Solution Type


Results

Result Bench Value NX NastranVon Mises Stress, grid point 1 (psi) 1111. 1111.




Result Bench Value NX NastranDeflection in X, grid point 2 (in) 0.01111 0.01093Reaction in X, grid point 1 (lb) –1.000E4 –1.000E4

References

Beer and Johnston. Mechanics of Materials.. New York: McGraw-Hill, Inc., 1992. p. 76.

Distributed Loads on a Cantilever Beam

Determine the deflection of a beam at the free end. Determine the stress at the midpoint of thebeam and the reaction force at the restrained end.


Input Files

mstvl003.dat

Units

Inch

Model Geometry

Length = 480 in.


• Area = 900 in.2

• Square cross section (30 in. x 30 in.)

• Iy = Iz = 67500 in.4




Material Properties

• E = 30E06 psi


Create eight successive linear beam (CBAR) elements along the X axis.

Boundary Conditions

• Restraints


• Loads

o Define a distributed load of 250 lb/in. in the –Y direction.

Solution Type


Results

Result Bench Value NX NastranX Stress at grid point 1 (psi) 6,400. 6,383.Deflection Magnitude at grid point 5 (in) 0.8190 0.8225 *Reaction Force Magnitude at grid point 1 (lb) 1.200E5 1.200E5

* Includes shear deformation which is neglected in theoretical value.

References


Moment Load on a Cantilever Beam

Determine the deflection of a beam at the free end. Determine the bending stress of the beam andthe reaction force at the restrained end.





Input Files

mstvl004.dat

Units

Inch

Model Geometry

Length = 480 in.


• Square cross section 30” x 30” inches

• Area = 900 in.2

• Iy = Iz = 67500 in.4

Material Properties

• E = 30E6 psi


Create eight successive linear beam (CBAR) elements along the X axis.

Boundary Conditions

• Restraints


• Loads




o Set the Z-moment of the end grid point to 2.5E6 in.-lb.

Solution Type


Results

Result Bench Value NX NastranVon Mises Stress at grid point 1 (psi) 555.6 555.6Deflection Magnitude at grid point 5 (in) 0.1422 0.1422Reaction Moment Z Direction at grid point 1(in.-lb)

2.500E6 2.499E6

* Includes shear deformation which is neglected in theoretical value.

References


Edge Pressure on Beam Element - Torque Loading

Determine the stress, elongation and resultant force due to a torque applied to a hollow cylinderat the free end.





Input Files

mstvl005.dat

Units

SI - meter

Model Geometry

Length = 1.5 m


• Radius1 = 0.02 m

• Radius2 = .03 m

Material Properties

• E = 208.6 GPa


• Create a CBAR element along the X axis.

• To find the maximum shearing stress, set the effective radius in torsion to 0.03 m.

• The minimum shearing stress is located at a radius equal to 0.02 m.

Boundary Conditions

• Restraints


• Loads

o Apply an edge torque equal to 4.08 kN-m along the 10 cm linear beam (CBAR) elementfurthest from the restrained end.

Solution Type


Results

Result Bench Value NX NastranMax Torsional Shear Stress (MPa) 120.0 120.0

Min Torsional Shear Stress (MPa) 80.00 80.00




Post Processing

To obtain the minimum and maximum shear stress values, a post processor which supports contourplots of the torsional shear stress on the cross section using the linear beam (CBAR) element forcesmust be used. The cross section location can be anywhere except the free end of the beam.

References


Thermal Strain, Displacement, and Stress on Heated Beam

A beam originally 1 meter long and at –50° C is heated to 25° C. First, determine the displacementand thermal strain on a cantilever beam. Fix the beam at the free end and then determine thedisplacement, reaction forces, and stresses along the beam. Next, fix the beam at both ends.


Input Files

mstvl007.dat

Units

SI - meter

Model Geometry

Length = 1 m


• Area = 0.01 m2




Material Properties

• E = 2.068E11 Pa

• Coefficient of thermal expansion = 1.2E–05

• v = 0.3


• Create 10 linear beam (CBAR) elements on the X axis and restrain the end grids in all directions.

• Apply a temperature on all grid points.

Boundary Conditions

• Restraints

o Case 1: Restrain one end of the beam in all six directions.

o Case 2: Restrain both ends of the beam in all six directions.

• Loads

o Set grid temperatures to 25°C. Set the reference temperature to –50°C.

Solution Type


Results

Case 1

Result Bench Value NX NastranX Displacement at grid 11 (m) .0009000 .0009000Axial Thermal Strain .0009000 .0009000

Case 2

Result Bench Value NX NastranX Displacement (m) 0 0Axial Stress (Pa) 1.860E8 1.861E8X Reaction Force (N) 1.860E6 1.861E6

References





Uniformly Distributed Load on Linear Beam

A beam 40 feet long is restrained and loaded as shown with a distributed load of 10,000 lb/ft.Determine the bending stress and the deflection at the middle of the beam.


Input Files

mstvl008.dat

Units

Inch

Model Geometry

Length = 480 in.





• Rectangular cross section (1.17 in. x 43.24 in.)

• Iz = 7892 in.4

Material Properties

• E = 30E06 psi


Create 4 successive linear beam (CBAR) elements that are each 10 feet long.

Boundary Conditions

• Restraints

o Restrain the second and the fourth grids in five degrees of freedom. Do not restrain rotationabout Z.

• Loads

o Define a distributed load (force per unit length) of –10,000 lb/foot (global negative Ydirection) on the end elements.

Solution Type


Results

Result Bench Value NX NastranY Displacement at grid 3 (in.) 0.1820 0.182Max bending stress (psi) 1.644E4 1.644E4

References


Membrane Loads on a Linear Quadrilateral Thin Shell Element

A circle is scribed on an unstressed aluminum plate. Forces acting in the plane of the plate causenormal stresses. Determine the change in the length of diameter AB and of diameter CD.





Element Types

cquad4

Input Files

mstvl009.dat

Units

Inch

Model Geometry

• Length = 15 in.

• Diameter = 9 in.

• Thickness = 3/4 in.




Material Properties

• E = 10E06 psi

• Poisson's ratio = 1/3

• F(x)/L = 9,000 lb/in.

• F(z)/L = 15,000 lb/in.


Create 1/4 of the model and apply symmetry boundary conditions. Then multiply the answer by 2 forcorrect results. Remember to account for the ratio of the circle diameter to plate length.

Boundary Conditions

• Restraints


• Loads

o Set the edge pressure to 9,000 lb/in. in the X direction and 15,000 lb/in. in the Z direction.

Solution Type


Results

Result Bench Value NX NastranX Diameter Change (in.) 4.800E-3 4.800E-3Z Diameter Change (in.) 14.40E-3 14.40E-3

Post Processing

• (dx at grid point 7 – dx at grid point 10) x 2 = (0.004 – 0.0016) x 2 = 0.0048

• (dz at grid point 7 – dz at grid point 24) x 2 = (0.012 –0.0048) x 2 = 0.0144

References


Axial Loading on Rod Element

Determine the stress, elongation, and strain due to an axial load on a rod element.





Input Files

mstvl011.dat

Units

SI - meters

Model Geometry

Length = 10 m


• Area = 0.01 m2

Material Properties

• E = 200.0 GPa


Create a rod (CROD) element along the X axis.

Boundary Conditions

• Restraints

o Restrain an end of the rod in the 3 translational degrees.

• Loads

o Apply a grid point force in the positive X-direction of 500 kN.

Solution Type


Results

Result Bench Value NX NastranAxial Stress (MPa) 50.00 50.00Axial Strain 0.0002500 0.0002500Elongation (mm) 2.500 2.500

References





Stress on a Beam as It Expands and Closes a Gap

Determine the stress on a beam as it expands thermally and closes a 0.002 inch gap. It is initially at70 °F and is heated to 170 °F.


Input Files

mstvl013.dat

Units

Inch

Model Geometry

Length = 3 in.

Material Properties

• E = 1.05E07 psi

• Coefficient of thermal expansion = 1.25E–05 in./(in.–°F)


• Create a single linear beam (CBAR) element on the X axis.




• Create an MPC to define the closing of the gap.

Boundary Conditions

• Restraints

o Restrain the free end of the beam in all six degrees.

• Loads

o Set grid temperature to 170 °F.

o Set the reference temperature to 70 °F.

Solution Type


Results

Result Bench Value NX NastranAxial Stress (psi) –6.125E3 –6.125E3

References

Harris, C. O. Introduction to Stress Analysis 1959. p. 58.

Thin Wall Cylinder in Pure Tension

Determine the stress and deflection of a thin wall cylinder with a uniform axial load.





Input Files

mstvl014.dat

Units

Inch

Model Geometry

• R = 0.5 in.

• Thickness = 0.01 in.

• y = 1.0 in.

Material Properties

• E = 10,000 psi




• ν = 0.3


Create 1/4 model of the cylinder with thin shell linear quadrilateral (CQUAD4) elements and symmetryboundary conditions.

Boundary Conditions

• Restraints

o Restrain edges of symmetry, in translation, in hoop direction, and rotation about Z axis.

o Restrain one end in Y direction.

Loads

o Apply membrane edge pressure of p / (pi)D = 3.1831 where p = 10 psi

Solution Type


Results

Result Bench Value NX NastranAxial (Z) Stress (psi) 1.000E3 1.000E3Axial (Z) Deflection (in.) 0.100 0.100Radial Deflection (in.) –0.01500 –0.01500

References

Roark, R. and Young, W. Formulas for Stress and Strain, 6th Edition. New York: McGraw-Hill BookCompany, 1989. p. 518, Case 1a.

Thin-walled Cantilever Beam in Bending

Determine the maximum stress, maximum deflection, and strain energy for a thin-walled cantileverbeam subjected to a bending load.





Input Files

mstvl015.dat

Units

Inch

Model Geometry

• Length = 30 in.

• Width = 5 in.

• Thickness = 0.1 in.

Material Properties

• E = 30E06 psi

• ν = 0.03





Create a 30 in. x 5 in. plate with thing shell (CQUAD4) elements.

Boundary Conditions

• Restraints

o Restrain at one of the ends in all directions.

• Loads

o Apply edge pressure of p/w = 1.2 lbs/in. where p = 6.0 lb.

Solution Type


Results

Result Bench Value NX NastranMax Deflection (in.) 4.320 4.264Max Bending Stress (psi) 2.160E4 1.980E4Total Strain Energy (lb in.) 12.96 12.79

References

Shigley, J. and Mitchel L. Mechanical Engineering Design, 4th Edition. New York: McGraw-Hill,Inc., 1983. pg. 804.

Strain Energy of a Truss

Determine the strain energy of a truss. The cross-sectional area of the diagonal members is twicethe cross-sectional area of the horizontal and vertical members.





Input Files

mstvl016.dat

Units

Inch

Model Geometry

• Length = 10 in.


• Cross-sectional area (A) = 0.01 in.2

Material Properties

• E = 30E06 psi


Create truss shown using rod (CROD) elements.

Boundary Conditions

• Restraints

o Restrain far left grid in directions: X, Y, Z, RX, RY.

o Restrain far right grid in directions: Y, Z, RX, RY.

• Loads




o Apply grid force in Y direction on lower center grid; F= 300 lb.

Solution Type


Results

Result Bench Value NX Nastran

Total Strain Energy (lb in.) 5.846 5.846

References




Chapter 3: Linear Statics Verification Using StandardNAFEMS Benchmarks

3.1 Overview of Linear Statics Verification Using Standard NAFEMSBenchmarksThe purpose of these linear statics test cases is to verify the function of NX Nastran using standardbenchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards,National Engineering Laboratory, Glasgow, U.K.).

These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elementsin commercial software. All results obtained using NX Nastran compare favorably with othercommercial finite element analysis software.


Each test case is structured with the following information:

• Test case data and information



o Units

o Finite element modeling information

o Boundary conditions (loads and restraints)

o Solution type

• Results

• Reference

Reference

The following reference has been used in these test cases:

NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks. Glasgow:NAFEMS, Rev. 3, 1990.


Chapter 3: Linear Statics Verification Using Standard NAFEMS Benchmarks

Test Cases

Elliptic Membrane

This test is a linear elastic analysis of an elliptic membrane (shown below) using coarse and finemeshes of plane stress elements and thin shell elements. It provides the input data and resultsfor NAFEMS Standard Benchmark Test LE1.

Ellipses:


Input Files

le101.dat (plane stress quadrilateral)

le102.dat (plane stress triangle)

le103.dat (thin shell)

Physical and Material Properties

• Thickness = 0.1 m

• Isotropic material

• E = 210E3 MPa

• v = 0.3

Units

SI



Linear Statics Verification Using Standard NAFEMS Benchmarks


• Plane stress (only MID1 defined on PSHELL) linear (CQUAD4) and parabolic (CQUAD8)quadrilaterals — coarse and fine mesh.

• Plane stress (only MID1 defined on PSHELL) linear (CTRI3) and parabolic (CTRI6) triangles— coarse and fine mesh.

• Thin shell (MID1, MID2 and MID3 defined on PSHELL) linear (CQUAD4) and parabolic(CQUAD8) quadrilaterals — coarse and fine mesh.

• The fine mesh is created by approximately halving the coarse mesh.




Boundary Conditions

• Uniform outward pressure at outer edge BC = 10 MPa

• Inner curved edge AD unloaded

• X displacement (edge AB) = 0




• Y displacement (edge CD) = 0

Solution Type


Results

Output — tangential edge stress at D (stress in Y direction)

Plane Stress Elements

Test case Grid point # Bench Value NX NastranLinear quad — coarse mesh 4 92.7 62.1Linear quad — fine mesh 204 92.7 79.6

Parabolic quad — coarse mesh 104 92.7 82.1Parabolic quad — fine mesh 304 92.7 89.9Linear triangle — coarse mesh 4 92.7 52.9Linear triangle — fine mesh 204 92.7 70.8Parabolic triangle — coarse mesh 104 92.7 76.8Parabolic triangle — fine mesh 304 92.7 93.6

Thin Shell Elements

Test case Grid point # Bench Value NX NastranLinear quad — coarse mesh 4 92.7 62.1Linear quad — fine mesh 204 92.7 79.6Parabolic quad — coarse mesh 104 92.7 82.1Parabolic quad — fine mesh 304 92.7 89.9




References

NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, Test No. LE1.Glasgow: NAFEMS, Rev. 3, 1990.

Cylindrical Shell Patch Test

This test is a linear elastic analysis of a cylindrical shell (shown below) using thin shell elements andtwo different loadings. It provides the input data and results for NAFEMS Standard BenchmarkTest LE2.


Input Files

• le201a.dat (linear shell, case 1)

• le201b.dat (parabolic shell, case 1)

• le202a.dat (linear shell, case 2)

• le202b.dat (parabolic shell, case 2)







• E = 210E3 MPa

• v = 0.3

Units

SI


• Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals

Boundary Conditions

• Translations and rotations (edge AB) = 0

• Z translations and normal rotations (edge AD and edge BC) = 0

Case 1 loading:

• Uniform normal edge moment on DC = 1.0 kNm/m

Case 2 loading:

• Uniform outward normal pressure at mid-surface ABCD = 0.6 MPa

• Tangential outward normal pressure on edge DC = 60.0 MPa




Solution Type


Results

Output — outer (convex) surface (top shell surface) tangential stress at point E (grid point 2):

Test case Filename Bench Value NX NastranLinear quad – case 1 le201a 60.00 51.8Linear quad – case 2 le202a 60.00 51.1*Parabolic quad – case 1 le201b 60.00 56.4Parabolic quad – case 2 le202b 60.00 56.4** Since the shapes of the shells are an approximation to a cylindrical surface, an edge load willnot be in the correct direction. To get this result, the edge load must be input as grid forces in thetangential direction.

Post Processing

• Stress component: Y

• Results obtained on the element top surface in cylindrical coordinate system




References


Hemisphere-Point Loads

This test is a linear elastic analysis of hemisphere point loads (shown below) using coarse andfine meshes of thin shell elements. It provides the input data and results for NAFEMS StandardBenchmark Test LE3.


Input Files

• le301.dat (linear quad, coarse mesh)

• le302.dat (linear quad, fine mesh)

• le303.dat (parabolic quad, coarse mesh)




• E = 68.25 × 103 MPa




• v = 0.3

Units

SI


• Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh

• Equally spaced grid points on AC, CE, EA

• Point G at X = Y = Z = 10 /( 31/2) grid point 7

Boundary Conditions

• Edge AE symmetry about XZ plane (y = rotation x = rotation z = 0)

• Edge CE symmetry about YZ plane (x = rotation y = rotation z = 0)

• Point E (x = y = z = 0)

• All other displacements on edge AC are free.

• Concentrated radial load outward at A = 2KN

• Concentrated radial load inward at C = 2KN




Solution Type


Results

Output — X displacement at point A

Mesh Test Case Bench Value NX Nastranlinear quad — coarse mesh le301 0.185 0.1848linear quad — fine mesh le302 0.185 0.1865parabolic quad — coarse mesh le303 0.185 0.1416

References


Z-Section Cantilever

This test is a linear elastic analysis of a Z-section cantilever (shown below) using thin shell elements.It provides the input data and results for NAFEMS Standard Benchmark Test LE5.





Input Files

• le501.dat (linear quadrilateral)

• le502.dat (parabolic quadrilateral)




• E = 210E3 MPa

• v = 0.3

Units

SI


• Thin shell linear (CQUAD4) and parabolic (CQUAD8) quadrilaterals

Boundary Conditions

• All displacements on edges B1, B2, B3 = 0

• Torque of 1.2MN applied at end C by two edge shears (at C1 & C3) of 0.6 MN




Solution Type


Results

Output — averaged axial stress at mid-surface, point A, grid point 30 (compression)

Result Bench Value NX NastranLinear quad - point A/grid point 30 –108.0 –111.0Parabolic quad - point A/grid point 30 –108.0 –110.3

References

NAFEMS Finite Element Methods & Standards. The Standard NAFEMS Benchmarks, Test No. LE5.Glasgow: NAFEMS, Rev. 3, 1990.

Skew Plate Normal Pressure

This test is a linear elastic analysis of a plate (shown below) using thin shell elements. It provides theinput data and results for NAFEMS Standard Benchmark Test LE6.


Input Files

• le601.dat (linear and parabolic quad)




• le602.dat (linear and parabolic triangle)




• E = 210E3 MPa

• v = 0.3

Units

SI


• Thin shelllinear (CQUAD4) and parabolic (CQUAD8) quadrilaterals — coarse and fine mesh

• Thin shell linear (CTRI3) and parabolic (CTRI6) triangles — coarse and fine mesh

Boundary Conditions

• Simple supports

• Z displacement = 0

• Normal pressure = –0.7KPa in the Z direction

Solution Type


Results

Output — maximum principal stress on the bottom surface at the plate center.

Case le601

Mesh Grid point # Bench Value NX NastranLinear quad coarse mesh 9 0.802 0.325Linear quad fine mesh 18 0.802 0.683Parabolic quad coarse mesh 43 0.802 0.625




Mesh Grid point # Bench Value NX NastranParabolic quad fine mesh 52 0.802 0.719

Case le602

Mresh Grid point # Bench Value NX NastranLinear triangle coarse mesh 9 0.802 0.396Linear triangle fine mesh 18 0.802 0.720Parabolic triangle coarse mesh 43 0.802 0.926Parabolic triangle fine mesh 52 0.802 0.857

References


Thick Plate Pressure

This article provides the input data and results for NAFEMS Standard Benchmark Test LE10. This testis a linear elastic analysis of a thick (shown below) using coarse and fine meshes of solid elements.

Ellipses:


Input Files

• le1001.dat (linear and parabolic brick)

• le1002.dat (linear and parabolic wedge)




• le1003.dat (linear and parabolic tetrahedron)

• le1004.dat (linear and parabolic pyramid)



• E = 210E3 MPa

• v = 0.3

Units

SI


• Solid brick (CHEXA) linear and parabolic - coarse and fine mesh

• Solid wedge (CPENTA) linear and parabolic - coarse and fine mesh

• Solid tetrahedron (CTETRA) - linear and parabolic - coarse and fine mesh

• Solid pyramid (CPYRAM) linear and parabolic - coarse and fine mesh (created by dividing eachlinear and parabolic brick element into 6 pyramid elements)

Solid Brick




Solid Wedge

Solid Tetrahedron — fine mesh only

Boundary Conditions

• Uniform normal pressure on the upper surface of the plate = 1 MPa

• Inner curved edge AD unloaded

• X and Y displacements on faces DCD'C′ and ABA′B′ = 0

• X and Y displacements on face BCB′C′ are fixed




• Z displacements along mid-plane are fixed

Solution Type


Results

Output — direct stress at point Dσyy

Test Case le1001

Mesh Grid point # Bench Value NX NastranLinear brick — coarse mesh 4 –5.50 –5.41Linear brick — fine mesh 204 –5.50 –5.67Parabolic brick — coarse mesh 104 –5.50 –6.13Parabolic brick — fine mesh 304 –5.50 –6.04

Test Case le1002

Mesh Grid point # Bench Value NX NastranLinear wedge — coarse mesh 4 –5.50 –5.94Linear wedge — fine mesh 204 –5.50 –5.83Parabolic wedge — coarse mesh 104 –5.50 –5.32Parabolic wedge — fine mesh 304 –5.50 –6.01

Test Case le1003

Result Grid point # Bench Value NX NastranLinear tetra — fine mesh 40 –5.50 –2.41Parabolic tetra — fine mesh 171 –5.50 –5.28




Test Case le1004

Mesh Grid point # Bench Value NX NastranLinear pyramid — coarse mesh 4 –5.50 –2.85Linear pyramid — fine mesh 204 –5.50 –3.83Parabolic pyramid — coarsemesh

104 –5.50 –5.60

Parabolic pyramid — fine mesh 304 –5.50 –5.72

References


Solid Cylinder/Taper/Sphere — Temperature

This test is a linear elastic analysis of a solid cylinder with a temperature gradient (shown below)using coarse and fine meshes of solid elements. It provides the input data and results for NAFEMSStandard Benchmark Test LE11.


Input Files

• le1101a.dat (linear brick — coarse mesh)




• le1101b.dat (linear brick — fine mesh)

• le1102a.dat (parabolic brick — coarse mesh)

• le1102b.dat (parabolic brick — fine mesh)

• le1103a.dat (linear wedge — coarse mesh)

• le1103b.dat (linear wedge — fine mesh)

• le1104a.dat (parabolic wedge — coarse mesh)

• le1104b.dat (parabolic wedge — fine mesh)

• le1105a.dat (linear tetra — coarse mesh)

• le1105b.dat (linear tetra — fine mesh)

• le1106a.dat (parabolic tetra — coarse mesh)

• le1106b.dat (parabolic tetra — fine mesh)

• le1107a.dat (linear pyramid — coarse mesh)

• le1107b.dat (linear pyramid — fine mesh)

• le1108a.dat (parabolic pyramid — coarse mesh)

• le1108b.dat (parabolic pyramid — fine mesh)



• E = 210E3 MPa

• v = 0.3

• a = 2.3E–4 °C

Units

SI


• Solid brick (CHEXA) linear and parabolic — coarse and fine mesh

• Solid wedge (CPENTA) linear (6 grid point) and parabolic (15 grid point) — coarse and fine mesh

• Solid tetrahedron (CTETRA) linear and parabolic — coarse and fine mesh

• Solid pyramid (CPYRAM) linear and parabolic — coarse and fine mesh (created by dividing eachlinear and parabolic brick element into 6 pyramid elements)




Solid Brick

Solid Tetrahedron




Boundary Conditions

• Linear temperature gradient in the radial and axial direction

T° C = (X2 + Y2)1/2 + Z

• X, Y, and Z displacements = 0

• X and Y displacements on face BCB′C′ are fixed

• Z displacements on XY-plane face and HIH′I′ face = 0

Solution Type


Results

Output - direct stress σyy at point A

File Name Result Grid point atPoint A

BenchValue

NXNastran

le1101a Linear brick — coarse mesh 30 –105.0 –88.50le1101b Linear brick — fine mesh 71 –105.0 –98.3le1102a Parabolic brick — coarse mesh 67 –105.0 –100.4le1102b Parabolic brick — fine mesh 159 –105.0 –111.2le1103a Linear wedge — coarse mesh 33 –105.0 –10.0le1103b Linear wedge — fine mesh 74 –105.0 –48.3le1104a Parabolic wedge — coarse mesh 71 –105.0 –87.2le1104b Parabolic wedge — fine mesh 187 –105.0 –96.2le1105a Linear tetra — coarse mesh 8 –105.0 –31.4




File Name Result Grid point atPoint A

BenchValue

NXNastran

le1105b Linear tetra — fine mesh 8 –105.0 –65.2le1106a Parabolic tetra — coarse mesh 8 –105.0 –89.6le1106b Parabolic tetra — fine mesh 8 –105.0 –97.3le1107a Linear pyramid — coarse mesh 30 –105.0 –57.0le1107b Linear pyramid — fine mesh 71 –105.0 –79.8le1108a Parabolic pyramid — coarse mesh 67 –105.0 –65.8le1108b Parabolic pyramid — fine mesh 159 –105.0 –108.8

References




Chapter 4: Normal Mode Dynamics Verification

4.1 Overview of Normal Mode Dynamics Verification UsingTheoretical SolutionsThe purpose of these normal mode dynamics test cases is to verify the function of NX Nastran usingtheoretical solutions. The test cases are relatively simple in form and most of them have closed-formtheoretical solutions.

The theoretical solutions shown in these examples are from well known engineering texts. For eachtest case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic.

The finite element method is very flexible in the types of physical problems represented. Theverification tests provided are not exhaustive in exploring all possible problems, but representcommon types of applications.

This overview provides information on the following:

• Understanding the test case format

• Understanding comparisons with theoretical solutions

• References






o Units

o Solution type

o Boundary conditions (loads and restraints/constraints)

• Results

• Reference

Understanding Comparisons with Theoretical Solutions

While differences in finite element and theoretical results are, in most cases, negligible, some testswould require an infinite number of elements to achieve the exact solution. Elements are chosen toachieve reasonable engineering accuracy with reasonable computing times.



Results reported here are results which you can compare to the referenced theoretical solution.Other results available from the analyses are not reported here. Results for both theoretical and finiteelement solutions are carried out with the same significant digits of accuracy.

The closed-form theoretical solution may have restrictions, such as rigid connections, that do notexist in the real world. These limiting restrictions are not necessary for the finite element model, butare used for comparison purposes. Verification to real world problems is more difficult but should bedone when possible.

The actual results from NX Nastran may vary insignificantly from the results presented in thisdocument. This variation is due to different methods of performing real numerical arithmetic ondifferent systems. In addition, it is due to changes in element formulations which have been made toimprove results under certain circumstances.

Reference

The following references have been used in the normal mode dynamics analysis verificationproblems presented:

1. Blevins, R. Formulas For Natural Frequency and Mode Shape, 1st Edition. New York: VanNorstrand Reinhold Company, 1979.

2. Timoshenko and Young. Vibration Problems in Engineering. New York: Van Norstrand ReinholdCompany, 1955.

3. Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, Theory and Applications. Boston: Allynand Bacon, Inc., 1978.

4. Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition. Boston: Allyn and Bacon,Inc., 1978.

Test Cases

Undamped Free Vibration — Single Degree of Freedom

Determine the natural frequency of the system shown.



Normal Mode Dynamics Verification


Input File

mstvn002.dat

Units

SI - meter

Model Geometry

• Length = 0.5 m

• a = 0.3 m

Physical Properties

• mass = 20 Kg

• k = 8 KN/m


• Create 5 rigid bar (RBAR) elements along the X axis. Each bar should be 0.1 m long.

• A lumped mass (CONM2) element is applied on the end grid point.




• A grid point-to-ground spring element (CELAS1) is applied 0.2 m from the lumped mass.

Boundary Conditions

• Restrain the first grid point to allow rotation only in the Z direction.

Solution Type

SOL 103 — Normal Mode Dynamics, Lanczos Method

Results

Result Bench Value NX NastranFrequency (Hz) 1.910 1.910

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, Theory and Applications, p. 75. Boston:Allyn and Bacon, Inc., 1978.

Two Degrees of Freedom Undamped Free Vibration — Principle Modes

Determine the natural frequencies of a dynamic system with two degrees of freedom.





Input File

mstvn003.dat

Units

SI- meter

Element Types

• Translational springs (CELAS1)

• Lumped mass (CONM2)




Physical Properties

• Mass = 1 kg

• k = 1 N/m


• Create four grid points on the Y axis.

• Create three linear springs (CELAS1) with stiffness of 1 N/m and with a uniaxial stiffnessreference coordinate system.

• Create two lumped mass elements (CONM2) with a mass of 1 kg.

Boundary Conditions

• Restrain ends in all directions.

• Restrain other grid points in all directions but Y.

Solution Type

Normal Mode Dynamics - SOL 103, Lanczos method

Results

Result Bench Value NX NastranFrequency of Mode 1 (Hz) 0.1592 0.1592Frequency of Mode 2 (Hz) 0.2757 0.2757

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, pp. 145-149. Boston: Allynand Bacon, Inc., 1978.

Three Degrees of Freedom Torsional System

Determine the natural frequencies of a dynamic system with three degrees of freedom.





Input File

mstvn004.dat

Element Types

• Rotational springs (CELAS1)


Units

SI — meter

Physical Properties

• J = J1 = J2 = J3 = 0.1

• k = k1 = k2 = k3 = 1 N*m


• Create four grid points on the X axis.

• Create three linear torsional springs (CELAS1) with stiffness of 1 N*m and with a stiffnessreference coordinate system being uniaxial.

• Create three lumped mass elements (CONM2) with a mass coordinate system = 1 and with massinertia system of: 0.1, 0.0, 0.0, 0.0, 0.0, 0.0.

Boundary Conditions

• Restrain one end in all directions.

• Restrain the other grid points in all directions but RX.

Solution Type

SOL 103 — Normal Mode Dynamics, Lanczos method

Results

Result Bench Value NX NastranFrequency of Mode 1 (Hz) 0.2240 0.2240Frequency of Mode 2 (Hz) 0.6276 0.6276Frequency of Mode 3 (Hz) 0.9069 0.9069

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, pp. 153-155. Boston: Allynand Bacon, Inc., 1978.




Two Degrees of Freedom Vehicle Suspension System

Determine the natural frequencies of dynamic system with two degrees of freedom. Degrees offreedom are one translational and one rotational.


Input Files

mstvn005.dat

Units

SI - meter

Physical Properties

• Mass = 1800 kg

• K1 = 42000 N/m

• K2 = 48000 N/m


• Create a linear translation spring (CELAS1) with stiffness of K1

• Create a linear translation spring (CELAS1) with stiffness of K2

• Create a lumped mass element (CONM2) with a mass coordinate system = 1 and mass inertiasystem of: 0.0, 0.0, 3528, 0.0, 0.0, 0.0.




• Create a three-noded rigid element (RBE2)

Boundary Conditions

• Nodal displacement restraints

o Restrain grid points 4 and 5 in all directions.

o Restrain the other grid points in all directions but Y and RZ.

Solution Type


Results

Result Bench Value NX NastranFrequency of Mode 1 (Hz) 1.086 1.086Frequency of Mode 2(Hz) 1.496 1.496

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations. Boston: Allyn and Bacon, Inc., 1978. pp.150-153.

Two Degrees of Freedom Vehicle Suspension System

Determine the natural frequencies of dynamic system with two degrees of freedom. Degrees offreedom are one translational and one rotational.





Input File

mstvn005.dat

Element Types

• Translational springs (CELAS1)


• Rigid (RBE2)

Units

SI — meter

Model Geometry

• Length1 = 1.6 m

• Length2 = 2.0 m

• r = 1.4 m (gyration radius; J = m*r*r)

Physical Properties

• mass = 1800 kg

• K1 = 42000 N/m

• K2 = 48000 N/m


• Create five grid points in the XY plane with the following coordinates:

o Grid point 1 = (0,0)

o Grid point 2 = (12,0)

o Grid point 3 = (–L1,0)

o Grid point 4 = (L2,–1)

o Grid point 5 = (–L1,–1)

• Create a linear translation spring (CELAS1) with stiffness of K1 between grid point 1 and gridpoint 5.

• Create a linear translation spring (CELAS1) with stiffness of K2 between grid point 2 and gridpoint 4.




• Create a lumped mass element (CONM2) with a mass coordinate system = 1 and mass inertiasystem of: 0.0, 0.0, 3528, 0.0, 0.0, 0.0.

• Create a three-grid-point rigid element (RBE2) using grid point 1, grid point 2, and grid point 3.

Boundary Conditions

• Restrain grid points 4 and 5 in all directions.

• Restrain the other grid points in all directions but Y and RZ.

Solution Type


Results

Result Bench Value NX NastranFrequency of Mode 1 (Hz) 1.086 1.086Frequency of Mode 2(Hz) 1.496 1.496

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, pp. 150-153. Boston: Allyn and Bacon,Inc., 1978.

Cantilever Beam Undamped Free Vibrations

Determine the natural frequencies of a cantilever beam.


Input File

mstvn006.dat

Element Type

Linear beam (CBEAM)




Units

Inch

Model Geometry

• Length = 100 in.

• Height = 2 in.


• w = 1 lb/in.

• J = .10

• Poisson's ratio = .3

Calculated Data

• A = h2 = 4 in2

• I = h4/12 = 1.33333

• G = E/2 × 1/1 + nu = 11538461.54

• m = w/g = 2.59067375E–3

• Ip = Ixx + Iyy = 2.66666


• Create 11 grid points on X axis.

• Create 10 linear beams (CBEAM) between grid points.

Boundary Conditions

• Restrain one end grid point in all directions.

Solution Type


Results

Result Bench Value NX NastranFrequency of Modes 1 & 2 (TransverseVibration)

6.953 6.953

Frequency of Modes 3 & 4 (TransverseVibration)

43.58 43.58

Frequency of Mode 5 (Torsional Vibration) 64.68 64.68




Result Bench Value NX NastranFrequency of Modes 6 & 7 (TransverseVibration)

122.0 122.0

Frequency of Mode 8 (Torsional Vibration) 193.9 195.7Frequency of Modes 9 & 10 (TransverseVibration)

238.8 239.3

References

Blevins, R. Formulas For Natural Frequency and Mode Shape, 1st Edition, pp. 108,193. New York:Van Norstrand Reinhold Company, 1979.

Natural Frequency of a Cantilevered Mass

Determine the natural frequencies of a dynamic system consisting of a massless beam and a lumpedmass at the end.


Input File

mstvn007.dat

Element Types

• Linear beam (CBAR)


Units

Inch

Model Geometry

Length = 30 in.


• Mass = 0.5 lbm




• E = 30E6 psi

• Density = 1.0E–6

• I = 1.5 in.4


• Create 2 grid points on the X axis with coordinates (0,0,0) and (30,0,0).

• Create a linear beam (CBAR) element between grid points with shear area ratio = 0.

• Create a lumped mass (CONM2) on one grid point with mass of 0.5 lbm.

Boundary Conditions

• Restrain wall end in all directions.

• Restrain mass end in directions of Z, RX, and RY.

Solution Type

SOL 103 — Normal Mode Dynamics, Lanczos method

Results

Result Bench Value NX NastranMode 2 Frequency (Hz) 15.92 15.92

References

Tse, F., Morse, I., and Hinkle, R. Mechanical Vibrations, 2nd Edition, p. 72. Boston: Allyn and Bacon,Inc., 1978.



Chapter 5: Normal Mode Dynamics Verification UsingStandard NAFEMS Benchmarks

5.1 Overview of Normal Mode Dynamics Verification Using StandardNAFEMS BenchmarksThe purpose of these normal mode dynamics test cases is to verify the function of NX Nastranusing standard benchmarks published by NAFEMS (National Agency for Finite Element Methodsand Standards, National Engineering Laboratory, Glasgow, U.K.).

These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elementsin commercial software. All results obtained using NX Nastran compare favorably with othercommercial finite element analysis software. Results of these test cases using other commercial finiteelement analysis software programs are available from NAFEMS.




o Units



o Boundary conditions (loads and restraints/constraints)

o Solution type

• Results

• Reference

Reference


NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis. Glasgow: NAFEMS, Nov., 1987.


Chapter 5: Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks

Beam Element Test Cases

Pin-ended Cross — In-plane Vibration

This test is a normal mode dynamic analysis of a pin-ended cross (shown below) using beamelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 1.

Attributes of this test are:

• Coupling between flexural and extensional behavior

• Repeated and close eigenvalues


Input Files

• nf001ac.dat (linear consistent)

• nf001al.dat (linear lumped)

Units

SI


• Area = .015625 m2

Shear ratio:

• Y = 0



Normal Mode Dynamics Verification Using Standard NAFEMS Benchmarks

• Z = 0

Material Properties

• E = 200E09 N/m2

• ρ=8000 kg/m3

• ν = 0.29 (Poisson's ratio)

• G = 8.01E10


• Four linear beam (CBAR) elements per arm

Boundary Conditions

• X = Y = 0 at A, B, C, D

• Z = Rx = Ry = 0 at all grid points

Solution Type


NX Nastran results were obtained in two different ways:

• Using lumped mass (lumped mass on, param coupmass = –1)

• Using coupled mass (lumped mass off, param coupmass = 1)




Results

Mode ReferenceValue (Hz)

NAFEMS TargetValue (Hz)

NX Nastran Result(lumped mass) (Hz)

NX Nastran Result(coupled mass) (Hz)

1 11.34 11.34 11.33 11.342, 3 17.71 17.69 17.66 17.694 17.71 17.72 17.69 17.725 45.35 45.48 45.02 45.526, 7 57.39 57.36 56.06 57.438 57.39 57.68 56.34 57.75

References

NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N.C.Selected Benchmarks for Natural Frequency Analysis Test No. 1. Glasgow: NAFEMS, Nov., 1987.

Pin-ended Double Cross - In-plane Vibration

This test is a normal mode dynamic analysis of a pin-ended double cross (shown below) using beamelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 2.








Input Files



Units

SI


Key-in section:

• Area = .015625 m2

Shear ratio:

• Y = 0

• Z = 0

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3



Boundary Conditions

• X = Y = 0 at A, B, C, D, E, F, G, H

• Z = Rx= Ry = 0 at all grid points




Solution Type



• Using lumped mass (lumped mass toggle on, param coupmass = –1)

• Using coupled mass (lumped mass toggle off, param coupmass = 1)

Results



NX Nastran Result(lumped mass)(Hz)

NX Nastran Result(coupled mass)(Hz)

1 11.34 11.34 11.33 11.342, 3 17.71 17.69 17.66 17.694, 5, 6, 7,8 17.71 17.72 17.69 17.729 45.35 45.48 45.02 45.5210, 11 57.39 57.36 56.06 57.4312, 13, 14, 15,16

57.39 57.68 56.34 57.75

References

NAFEMS Finite Element Methods & Standards. Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis, Test No. 2. Glasgow: NAFEMS, Nov., 1987.




Free Square Frame - In-plane Vibration

This test is a normal mode dynamic analysis of a free square frame (shown below) using beamelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 3.



• Rigid body modes (3 modes)



Input Files



Units

SI


Shear ratio:

• Y = 1.0

• Z = 1.0

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3






Boundary Conditions

• Rotations fixed, translations free

Solution Type



• Using lumped mass (lumped mass toggle on, param coupmass = –1)

• Using coupled mass (lumped mass toggle off, param coupmass = 1)

Results



NX NastranResult (lumpedmass) (Hz)


4 3.261 3.262 3.259 3.2595 5.668 5.665 5.660 5.6636, 7 11.14 11.15 10.89 11.138 12.85 12.83 12.74 12.809 24.57 24.66 23.53 24.6410, 11 28.70 28.81 28.13 28.73

References





Cantilever with Off-center Point Masses

This test is a normal mode dynamic analysis of a cantilever with off-center point masses (shownbelow) using beam elements. This document provides the input data and results for NAFEMSSelected Benchmarks for Natural Frequency Analysis,Test 4.


• Coupling between torsional and flexural behavior

• Inertial axis non-coincident with flexibility axis

• Discrete lumped mass, rigid links

• Close eigenvalues


Input Files

• nf004a.dat

Units

SI


Shear ratio:

• Y = 1.128

• Z = 1.128

Material Properties

• E = 200E09 N/m 2

• ρ = 8000 kg/m3

• ν = 0.3





• Five linear beam (CBAR) elements along cantilever

Boundary Conditions

• X = Y = Z = Rx = Ry = Rz = 0 at A

Solution Type

SOL 103 — Normal Mode Dynamics, Lanczos (Parameter COUPMASS = –1)

Results

Mode Reference Value(Hz)

NAFEMS Target Value(Hz)

NX Nastran Result (Hz)

1 1.723 1.723 1.7142 1.727 1.727 1.7203 7.413 7.413 7.5544 9.972 9.972 9.9545 18.16 18.16 17.686 26.96 26.97 26.78

References


Deep Simply-Supported Beam

This test is a normal mode dynamic analysis of a deep simply supported beam (shown below).This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 5.





• Shear deformation and rotary inertial (Timoshenko beam)

• Possibility of missing extensional modes when using iteration solution methods

• Repeated eigenvalues


Input Files

• nf005ac.dat (linear consistent, param coupmass = 1)

• nf005al.dat (linear lumped, param coupmass = –1)

Units

SI


Shear ratio:

• Y = 1.176923

• Z = 1.176923

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


• Five linear beam elements (CBEAM)

Boundary Conditions

• X = Y = Z = Rx =0 at A




• Y = Z = 0 at B

Solution Type



• Using lumped mass (lumped mass on, param coupmass = –1)

• Using coupled mass (lumped mass off, param coupmass = 1)

Results





1, 2 (flexural) 42.65 42.57 43.15 43.263 (torsional) 77.54 77.84 77.20 77.844 (extensional) 125.0 125.5 124.5 125.55, 6 (flexural) 148.3 145.5 149.8 154.97 (torsional) 233.1 241.2 224.1 241.28, 9 (flexural) 284.6 267.0 271.0 306.7

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis, Test No. 5. Glasgow: NAFEMS, Nov., 1987.

Circular Ring — In-plane and Out-of-plane Vibration

This test is a normal mode dynamic analysis of a circular ring (shown below) using beam elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 6.





• Rigid body modes (six modes)



Input Files

• nf006ac.dat (param coupmass = 1)

• nf006al.dat (param coupmass = –1)

Units

SI


Shear ratio:

• Y = 1.128205

• Z = 1.128205

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


• 20 linear beam (CBAR) elements




Boundary Conditions

• X = Y = Z = Rx = Ry = Rz active

• Model is unsupported.

Solution Type


NX Nastran results were obtained two different ways:

• Using coupled mass (param coupmass = –1)

• Using lumped mass (param coupmass = 1)

Results





7, 8 (out ofplane)

51.85 52.29 51.62 52.38

9, 10 (in plane) 53.38 53.97 54.05 53.8011, 12 (out ofplane)

148.8 149.7 146.9 149.7

13, 14 (in plane) 151.0 152.4 152.2 151.515, 16 (out ofplane)

287.0 288.3 280.4 287.3

17, 18 (in plane) 289.5 288.3 289.2 289.1

References


Cantilevered Beam

This test is a normal mode dynamic analysis of a cantilevered beam (shown below). This documentprovides the input data and results for NAFEMS Selected Benchmarks for Natural FrequencyAnalysis, Test 71.





• Ill-conditioned stiffness matrix


Input Files

• nf071a.dat (Test 1)

• nf071b.dat (Test 2)

• nf071c.dat (Test 3)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ=8000 kg/m3


Three tests — all use linear beam (CBAR) elements

• Test 1: a = b

• Test 2: a = 10b

• Test3: a = 100b

Boundary Conditions

• X = Y = Rz = 0 at A

• Z = 0 at all grid points

• Rx = Ry = 0 at all grid points




Solution Type


Beams always use a coupled mass formulation (param coupmass = 1).

Results

Mode Reference Value (Hz) Mesh NX Nastran Result (Hz)1 1.010 a = b

a = 10b

a = 100b

1.010

1.010

1.0102 6.327 a = b

a = 10b

a = 100b

6.324

6.327

6.3303 17.72 a = b

a = 10b

a = 100b

17.70

17.80

17.834 34.72 a = b

a = 10b

a = 100b

34.70

34.86

35.075 57.39 a = b

a = 10b

a = 100b

57.48

60.64

64.826 85.73 a = b

a = 10b

a = 100b

86.24

101.86

104.74

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis Test No. 71. Glasgow: NAFEMS, Nov., 1987.

Shell Element Test Cases

Thin Square Cantilevered Plate — Symmetric Modes

This test is a normal mode dynamic analysis of a thin, square, cantilevered plate meshed with NXNastran shell elements. This document provides the input data and results for NAFEMS SelectedBenchmarks for Natural Frequency Analysis, Test 11a.





• Symmetric modes, symmetric boundary conditions along the cutting plane


Input Files

• nf011a_l.dat (4-noded quadrilateral, lumped mass)

• nf011a_c.dat (4-noded quadrilateral, coupled mass)

• nf011ha_l.dat (8-noded quadrilateral, lumped mass)

• nf011ha_c.dat (8-noded quadrilateral, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:

• 32 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.05m

• 8 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05m




Boundary Conditions

• X = Y = Rz = 0 at all grid points

• Z = Ry = Rx = 0 along Y-axis

• Rx = 0 along Y = 5m

Solution Type


Results were obtained in two different ways:

• Using lumped mass (param coupmass = –1)

• Using coupled mass (param coupmass = 1)

Results


Mesh NX NastranResult (lumpedmass)(Hz)

NX NastranResult (coupledmass(Hz)

1 0.4210 Linear

Parabolic

0.4150

0.4150

0.4180

0.4180





Mesh NX NastranResult (lumpedmass)(Hz)

NX NastranResult (coupledmass(Hz)

2 2.582 Linear

Parabolic

2.490

2.478

2.604

2.5673 3.306 Linear

Parabolic

3.115

3.134

3.314

3.2714 6.555 Linear

Parabolic

6.044

6.163

6.538

6.5395 7.381 Linear

Parabolic

7.094

7.099

7.808

7.4956 11.40 Linear

Parabolic

10.57

10.99

12.34

12.08

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis, Test No. 11a. Glasgow: NAFEMS, Nov., 1987.

Thin Square Cantilevered Plate — Anti-symmetric Modes

This test is a normal mode dynamic analysis of a thin, square, cantilevered plate meshed with shellelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 11b.


• Anti-symmetric modes





Input Files

• nf011b.dat (linear (4-noded) quadrilateral)

• nf011hb.dat (parabolic (8-noded) quadrilateral)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:



Mesh only half the plate (10m × 5m).

Boundary Conditions


• Z = Ry = Rx = 0 along Y-axis

• Rx = 0 along Y = 5m




Solution Type



• Using lumped mass (param coupmass = —1)


Results


Mesh NAFEMSTarget Value(Hz)

NX NastranResult(lumpedmass)(Hz)

NX NastranResult(coupledmass(Hz)

1 1.029 Linear

Parabolic

1.019

1.018

1.000

1.005

1.020

1.0222 3.753 Linear

Parabolic

3.839

3.710

3.570

3.597

3.767

3.7253 7.730 Linear

Parabolic

8.313

7.768

7.091

7.026

8.113

7.7864 8.561 Linear

Parabolic

9.424

8.483

8.047

8.133

9.025

8.6905 not available Linear

Parabolic

11.73

11.19

9.940

10.15

11.69

11.196 not available Linear

Parabolic

17.82

15.76

14.22

14.21

17.44

16.78

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis Test No. 11b. Glasgow: NAFEMS, Nov., 1987.




Free Thin Square Plate

This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 12.


• Rigid body modes (three modes)



Input Files

• nf012l_l.dat (linear (4-noded) quadrilateral, lumped mass)

• nf012l_c.dat (linear (4-noded) quadrilateral, coupled mass)

• nf012h_l.dat (parabolic (8-noded) quadrilateral, lumped mass)

• nf012h_c.dat (parabolic (8-noded) quadrilateral, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:






Boundary Conditions


Solution Type


Results were obtained in two different ways:



Results



NX NastranResult(lumpedmass) (Hz)

NX NastranResult(coupledmass) (Hz)

4 1.622 Linear

Parabolic

1.632

1.532

1.578

1.584

1.624

1.6195 2.360 Linear

Parabolic

2.402

2.356

2.241

2.233

2.389

2.3636 2.922 Linear

Parabolic

3.006

2.861

2.804

2.808

2.979

2.9297, 8 4.233 Linear

Parabolic

4.251

4.122

3.931

3.944

4.237

4.1589 7.416 Linear

Parabolic

7.859

7.363

6.822

6.813

7.790

7.47710 Not available Linear

Parabolic

8.027

7.392

6.822

6.813

7.790

7.477




References


Simply Supported Thin Square Plate



• Well established



Input Files

• nf013l_l.dat (linear quadrilateral, lumped mass)

• nf013l_c.dat (linear quadrilateral, coupled mass)

• nf013h_l.dat (parabolic quadrilateral, lumped mass)

• nf013h_c.dat (parabolic quadrilateral, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Two tests:



Boundary Conditions


• Z = Rx = 0 along edges X = 0 and X = 10m

• Z = Ry = 0 along edges Y = 0 and Y = 10m

Solution Type





Results


Mesh NX Nastran Result(lumped mass)(Hz)


1 2.377 Linear

Parabolic

2.332

2.376

2.392

2.3822, 3 5.942 Linear

Parabolic

5.797

5.938

6.181

6.0264 9.507 Linear

Parabolic

8.963

9.747

9.933

10.22







5, 6 11.88 Linear

Parabolic

11.67

11.87

13.27

12.397, 8 15.45 Linear

Parabolic

14.45

16.56

17.07

18.17

References


Simply Supported Thin Annular Plate



• Curved boundary (skewed coordinate system)



Input Files

• nf014l_l.dat (linear quadrilateral, lumped mass)




• nf014l_c.dat (linear quadrilateral, coupled mass)

• nf014h_l.dat (parabolic quadrilateral, lumped mass)

• nf014h_c.dat (parabolic quadrilateral, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:

• 160 linear quadrilateral thin shell (CQUAD4) elements — thickness = 0.06 m

• 48 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.06 m

Boundary Conditions


• Z′ = Rx′ = 0 around the circumference

Solution Type








Results




1 1.870 Linear

Parabolic

1.859

1.840

1.877

1.8732, 3 5.137 Linear

Parabolic

5.293

5.111

5.249

5.1514, 5 9.673 Linear

Parabolic

10.03

9.673

9.983

9.7136 14.85 Linear

Parabolic

14.37

13.95

15.41

14.927, 8 15.57 Linear

Parabolic

16.10

15.55

15.55

15.719 18.38 Linear

Parabolic

18.07

17.38

19.09

18.52

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis,, Test No. 13. Glasgow: NAFEMS, Nov., 1987.

Clamped Thin Rhombic Plate






• Distorted elements


Input Files

• nf015l.dat linear (lumped)

• nf015ha.dat parabolic (lumped)

• nf015hb.dat parabolic (consistent)

• nf015hc.data linear (consistent)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:



Boundary Conditions


• Z′ = Rx′ = Ry′ = 0 along all four edges




Solution Type

SOL103 — Normal Mode Dynamics




Results





1 7.938 Linear

Parabolic

8.142

7.873

7.818

7.902

7.955

7.9292 12.84 Linear

Parabolic

13.89

12.48

12.83

12.85

13.39

13.013 17.94 Linear

Parabolic

20.04

17.31

17.81

17.95

19.07

18.474 19.13 Linear

Parabolic

20.17

18.74

18.55

18.96

19.24

19.175 24.01 Linear

Parabolic

27.70

27.95

23.67

23.88

26.19

25.236 27.92 Linear

Parabolic

32.05

25.88

27.70

27.91

29.82

28.81

References





Cantilevered Thin Square Plate with Distorted Mesh

This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements.This document provides the input data and results for NAFEMSSelected Benchmarks for NaturalFrequency Analysis, Test 16.


• Distorted meshes


Input Files

• nf016a1.dat: (16 parabolic quad, lumped mass)

• nf016a2.dat: (16 parabolic quad, coupled mass)

• nf016b1.dat: (16 parabolic quad, lumped mass)

• nf016b2.dat: (16 parabolic quad, coupled mass)

• nf016c1.dat: (4 parabolic quad, lumped mass)

• nf016c2.dat: (4 parabolic quad, coupled mass)

• nf016d1.dat: (4 parabolic quad, lumped mass)

• nf016d2.dat: (4 parabolic quad, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





All tests — parabolic quadrilateral thin shell elements — thickness = 0.05m

Four tests:

• Test 1 — 16 elements

• Test 2 — 16 elements with specified grid points at the following XY coordinates:

CoordinatesNode X Y1 4.000 4.0002 2.250 2.2503 4.750 2.5004 7.250 2.7505 7.500 7.2506 5.250 7.2507 5.250 7.2508 2.250 7.2509 2.500 4.750

• Test 3 — 4 elements




• Test 4 — 4 elements with a specified grid point at the following XY coordinate:

CoordinatesNode X Y1 4.000 4.000

Boundary Conditions

• X = Y = Z = Ry = 0 along Y-axis

Solution Type








Results


Test NAFEMSTarget Value(Hz)



1 0.4210 1

2

3

4

0.4174

0.4174

0.4144

0.4145

0.4139

0.4135

0.4021

0.4000

0.4181

0.4182

0.4189

0.41922 1.029 1

2

3

4

1.020

1.020

0.9990

1.002

0.9985

0.9967

0.9347

0.9202

1.024

1.024

1.021

1.0253 2.582 1

2

3

4

2.564

2.571

2.554

2.565

2.444

2.445

2.132

2.112

2.569

2.566

2.708

2.6984 3.306 1

2

3

4

3.302

3.317

3.401

3.424

3.082

3.072

2.707

2.697

3.281

3.280

3.449

3.4305 3.753 1

2

3

4

3.769

3.780

3.697

3.714

3.540

3.535

3.136

3.077

3.728

3.731

3.913

3.8816 6.555 1

2

3

4

6.805

6.883

5.455

5.133

6.018

5.994

5.458

5.459

6.551

6.552

7.108

6.858




References


Simply Supported Thick Square Plate, Test A

This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 21a.




• Effect of secondary restraints


Input Files

• nf021a.dat: linear (lumped mass)

• nf021ha.dat: parabolic (lumped mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Two tests:



Boundary Conditions

• Z = 0 along all four edges


• Rx = 0 along edges X = 0 and X = 10 m

• Ry = 0 along edges Y = 0 and Y = 10 m

Solution Type








Results





1 45.90 Linear

Parabolic

46.66

45.94

45.83

46.17

46.35

45.832, 3 109.4 Linear

Parabolic

115.8

110.4

110.6

110.3

114.1

109.44 167.9 Linear

Parabolic

177.5

170.4

164.8

167.3

174.3

169.85, 6 204.5 Linear

Parabolic

233.4

212.8

211.8

204.6

227.1

208.27, 8 256.5 Linear

Parabolic

283.6

270.0

250.5

249.3

276.9

268.49 336.6 Linear

Parabolic

371.1

344.8

313.1

311.4

364.3

319.410 336.6 Linear

Parabolic

371.1

344.8

338.4

347.6

385.8

319.4

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis, Test No. 21a. Glasgow: NAFEMS, Nov., 1987.

Simply Supported Thick Square Plate, Test B

This test is a normal mode dynamic analysis of a free thin square plate meshed with shell elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 21b.







• Effect of secondary restraints


Input Files

• nf021b_c.dat (quadrilateral thin shell elements — coupled mass)

• nf021b_l.dat (quadrilateral thin shell elements — lumped mass)

• nf021hb_c.dat (parabolic thin shell elements — coupled mass)

• nf021hb_l.dat (parabolic thin shell elements — lumped mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:

• 64 linear quadrilateral thin shell elements — thickness = 1.0 m

• 16 parabolic quadrilateral thin shell elements — thickness = 1.0 m




Boundary Conditions

• Z = 0 along all four edges; X = Y = Rz = 0 at all grid points

Solution Type








Results





1 45.90 Linear

Parabolic

44.75

44.13

44.65

44.82

44.96

44.492, 3 109.4 Linear \

Parabolic

112.9

107.9

109.1

108.5

112.3

107.64 167.9 Linear

Parabolic

170.3

164.2

161.4

163.6

170.2

165.75, 6 204.5 Linear

Parabolic

230.2

20.07

210.5

203.1

225.4

206.57, 8 256.5 Linear

Parabolic

274.2

260.3

247.1

245.7

272.5

263.69 336.6 Linear

Parabolic

356.0

342.8

308.8

307.2

358.4

318.610 336.6 Linear

Parabolic

356.0

342.8

337.6

346.9

384.8

318.6

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis, Test No. 21b. Glasgow: NAFEMS, Nov., 1987.

Clamped Thick Rhombic Plate






• Distorted elements


Input Files

• nf022l_l.dat

• nf022l_c.dat

• nf022h_l.dat

• nf022h_c.dat

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:

• 100 linear quadrilateral thin shell (CQUAD4) elements - thickness = 1.0 m

• 36 parabolic quadrilateral thin shell (CQUAD8) elements - thickness = 1.0 m




Boundary Conditions


• Z′ = Rx′ = Ry′ = 0 along all four edges

Solution Type

SOL 103 – Normal Mode Dynamics


• Using lumped mass (parm coupmass = –1)


Results





1 134.0 Linear

Parabolic

137.8

133.9

131.2

134.9

134.3

135.22 201.4 Linear

Parabolic

218.5

203.3

200.4

204.4

211.9

206.33 265.8 Linear

Parabolic

295.4

271.4

262.0

270.3

286.6

276.4








4 282.7 Linear

Parabolic

296.8

283.7

273.6

286.9

287.0

289.15 334.5 Linear

Parabolic

383.6

346.4

327.0

337.5

373.3

353.86 Not available Linear

Parabolic

426.6

386.6

372.2

384.7

410.6

394.0

References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N.C.,Selected Benchmarks for Natural Frequency Analysis, Test No. 22. Glasgow: NAFEMS, Nov.,1987.

Simply Supported Thick Annular Plate

This test is a normal mode dynamic analysis of a simply supported thick annular plate meshedwith shell elements. This document provides the input data and results for NAFEMS SelectedBenchmarks for Natural Frequency Analysis, Test 23.








Input Files

nf023l_l.dat

nf023l_c.dat

nf023h_l.dat

nf023h_c.dat

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:



Boundary Conditions


• Z′ = Rx′ = 0 around the circumference




Solution Type

SOL 103 — Normal Mode Dynamics



• Using coupled mass (param coupmas = 1)

Results




NX NastranResult(coupledmass(Hz)

1 18.58 Linear

Parabolic

18.82

18.59

18.40

18.53

18.64

18.652, 3 48.92 Linear

Parabolic

49.82

49.02

50.00

49.22

50.81

49.414, 5 92.59 Linear

Parabolic

96.06

92.90

93.09

93.41

96.00

93.736 140.2 Linear

Parabolic

148.3

140.9

134.6

140.2

147.0

143.17, 8 Not available Linear

Parabolic

153.7

146.6

144.0

147.0

152.1

148.29 166.4 Linear

Parabolic

174.5

167.3

162.2

166.9

177.1

170.4




References


Cantilevered Square Membrane

This test is a normal mode dynamic analysis of a cantilevered square membrane meshed with shellelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 31.




Input Files

• nf031l.dat (linear quadrilateral, lumped mass)

• nf031a.dat (linear quadrilateral, coupled mass)

• nf031h.dat (parabolic quadrilateral, lumped mass)

• nf031j.dat (parabolic quadrilateral, coupled mass)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Two tests:

• 64 linear quadrilateral thin shell (CQUAD4) elements - thickness = 0.05 m

• 16 parabolic quadrilateral thin shell (CQUAD8) elements - thickness = 0.05 m

Boundary Conditions

• X = Y = 0 along the Y axis


Solution Type








Results





1 52.40 Linear

Parabolic

52.91

52.64

52.48

52.30

52.78

52.602 125.7 Linear

Parabolic

126.1

125.9

125.6

125.7

126.1

125.93 140.8 Linear

Parabolic

143.2

141.5

139.6

139.5

142.9

141.44 222.5 Linear

Parabolic

228.9

224.6

215.1

214.4

227.5

224.35 241.4 Linear

Parabolic

247.9

243.3

240.1

242.3

247.4

242.96 255.7 Linear

Parabolic

260.6

256.8

252.4

254.6

259.8

256.6

References


Cantilevered Tapered Membrane

This test is a normal mode dynamic analysis of a cantilevered tapered membrane meshed with shellelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 32.





• Shear behavior

• Irregular mesh

• Symmetry


Input Files





Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:

• 128 linear quadrilateral thin shell (CQUADR) elements — thickness = 0.1 m





Boundary Conditions

• X = Y = 0 along the Y axis


Solution Type



• Using lumped mass (param coupmas = –1)


Results





1 44.62 Linear

Parabolic

44.91

44.64

44.66

44.54

44.78

44.632 130.0 Linear

Parabolic

132.1

130.1

130.3

129.7

131.8

130.13 162.7 Linear

Parabolic

162.8

162.7

162.6

162.7

162.8

162.74 246.1 Linear

Parabolic

253.0

246.6

246.1

245.1

252.3

246.45 379.9 Linear

Parabolic

393.3

382.0

377.9

377.9

393.2

381.4








6 391.4 Linear

Parabolic

396.3

391.6

389.7

390.9

395.0

391.5

References


Free Annular Membrane

This test is a normal mode dynamic analysis of a free annular membrane meshed with shell elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 33.





Input Files








Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Two tests:






Boundary Conditions


Solution Type








Results





4, 5 129.2 Linear

Parabolic

129.5

126.5

127.8

125.7

128.8

125.86 226.2 Linear

Parabolic

225.5

224.3

224.5

224.0

225.3

224.27, 8 234.7 Linear

Parabolic

234.9

233.0

229.9

230.8

234.9

233.09, 10 264.7 Linear

Parabolic

272.1

264.8

264.3

262.6

271.2

263.611, 12 336.6 Linear

Parabolic

340.3

335.7

329.0

331.5

339.9

335.713, 14 376.8 Linear

Parabolic

392.0

378.6

369.9

373.3

390.5

377.4

References


Cantilevered Thin Square Plate

This test is a normal mode dynamic analysis of a cantilevered thin square plate meshed with shellelements. This document provides the input data and results for NAFEMSSelected Benchmarks forNatural Frequency Analysis, Test 73.





Input Files

• nf073a.dat (Test 1)

• nf073b.dat (Test 2)

• nf073c.dat (Test 3)

• nf073d.dat (Test 4)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


16 parabolic quadrilateral thin shell (CQUAD8) elements — thickness = 0.05 m

Boundary Conditions

X = Y = Z = Ry = 0 along the Y axis




Solution Type





Results





1 0.4210 Test 1

Test 2

Test 3

Test 4

0.4174

0.4174

0.4175

0.4184

0.4154

0.4154

0.4154

0.4161

0.4183

0.4183

0.4184

0.41922 1.029 Test 1

Test 2

Test 3

Test 4

1.020

1.020

1.021

1.032

1.051

1.006

1.007

1.015

1.023

1.023

1.027

1.0243 2.582 Test 1

Test 2

Test 3

Test 4

2.564

2.597

2.677

2.850

2.485

2.509

2.524

2.563

2.579

2.605

2.675

2.6724 3.306 Test 1

Test 2

Test 3

Test 4

3.302

3.345

3.365

3.571

3.150

3.180

3.196

3.373

3.298

3.332

3.344

3.5355 3.753 Test 1

Test 2

Test 3

Test 4

3.769

3.888

4.035

5.466

3.622

3.713

3.828

4.935

3.765

3.862

4.000

5.360








6 376.8 Test 1

Test 2

Test 3

Test 4

6.805

7.517

7.495

——

6.292

6.901

6.879

——

6.719

7.399

7.387

——

References


Axisymmetric Solid and Solid Element Test Cases

Free Cylinder — Axisymmetric Vibration

This test is a normal mode dynamic analysis of a free cylinder meshed with axisymmetric elements.This document provides the input data and results for NAFEMS Selected Benchmarks for NaturalFrequency Analysis, Test 41.


• Rigid body modes (one mode)

• Coupling between axial, radial, and circumferential behavior

• Close eigenvalues


Input Files

• nf041l.dat (linear axisymmetric, lumped mass, CQUADX4)

• nf041lt.dat (linear axisymmetric, lumped mass, CTRAX3)

• nf041a.dat (linear axisymmetric, coupled mass, CQUADX4)




• nf041at.dat (linear axisymmetric, coupled mass, CTRAX3)

• nf041h.dat (parabolic axisymmetric, lumped mass, CQUADX8)

• nf041ht.dat (parabolic axisymmetric, lumped mass, CTRAX6)

• nf041j.dat (parabolic axisymmetric, coupled mass, CQUADX8)

• nf041jt.dat (parabolic axisymmetric, coupled mass, CTRAX6)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg / m3

• ν = 0.3


Four meshes:

• 48 axisymmetric solid linear quadrilateral (CQUADX4) elements

• 96 axisymmetric solid linear triangular (CTRAX3) elements

• 8 axisymmetric solid parabolic quadrilateral (CQUADX8) elements

• 16 axisymmetric solid parabolic triangular (CTRAX6) elements

Boundary Conditions

Unsupported

Solution Type








Results

Mode # ReferenceValue (Hz)



NX NastranResult (coupledmass) (Hz)

2 243.5 CQUADX4CTRAX3CQUADX8CTRAX6

244.0244.0243.5243.5

243.2243.3243.2243.4

244.0244.1243.5243.5


379.4379.4377.5377.5

370.9377.7356.5376.5

378.1380.9377.5377.5


395.4395.4394.3394.3

379.3391.4356.9385.7

394.4397.0394.3394.3


401.4401.4397.9397.9

385.9395.6375.9386.7

398.0408.7398.0398.1


421.9421.9406.4406.4

389.6423.0393.7397.1

406.8430.4406.4407.3

Note

The reference value refers to the accepted solution to the problem.

References


Thick Hollow Sphere — Uniform Radial Vibration

This test is a normal mode dynamic analysis of a thick hollow sphere meshed using axisymmetricelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 42.






• Constraint equations


Input Files

• nf042l.dat (linear axisymmetric, lumped mass, CQUADX4)

• nf042lt.dat (linear axisymmetric, lumped mass, CTRAX3)

• nf042a.dat (linear axisymmetric, coupled mass, CQUADX4)

• nf042at.dat (linear axisymmetric, coupled mass, CTRAX3)

• nf042h.dat (parabolic axisymmetric, lumped mass, CQUADX8)

• nf042ht.dat (parabolic axisymmetric, lumped mass, CTRAX6)

• nf042j.dat (parabolic axisymmetric, coupled mass, CQUADX8)

• nf042jt.dat (parabolic axisymmetric, coupled mass, CTRAX6)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Four meshes:

• 10 axisymmetric solid linear quadrilateral (CQUADX4) elements -α = 5°

• 20 axisymmetric solid linear triangular (CTRAX3) elements -α = 5°

• 10 axisymmetric solid parabolic quadrilateral (CQUADX8) elements -α = 5°

• 20 axisymmetric solid parabolic triangular (CTRAX6) elements -α = 5°

Boundary Conditions

• Z′ displacement = 0 at all grid points

• Grid points at the same R′ are constrained to have the same r′ displacement

• One constraint set

Solution Type








Results




NX NastranResult (coupledmass) (Hz)


370.6370.6370.0370.0

370.0370.5369.4369.7

370.0370.7369.8369.8


841.2841.2838.1838.1

831.8834.0832.7835.9

839.4842.7837.7837.7

3 1451. CQUADX4CTRAX3CQUADX8CTRAX6

1473.1473.1453.1453.

1421.1424.1434.1446.

1471.1475.1451.1451.


2192.2192.2132.2132.

2031.2033.2073.2105.

2189.2194.2117.2117.


2976.2976.2853.2853.

2604.2607.2706.2773.

2971.2978.2799.2799.

Note


References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.Selected Benchmarks for Natural Frequency Analysis Test No. 42. Glasgow: NAFEMS, Nov., 1987.

Simply Supported Annular Plate — Axisymmetric Vibration

This test is a normal mode dynamic analysis of a simply supported annular plate meshed withaxisymmetric elements. This document provides the input data and results for NAFEMS SelectedBenchmarks for Natural Frequency Analysis, Test 43.







Input Files

• nf043a.dat (linear axisymmetric, lumped mass, CQUADX4)

• nf043at.dat (linear axisymmetric, lumped mass, CTRAX3)

• nf043b.dat (linear axisymmetric, coupled mass, CQUADX4)

• nf043bt.dat (linear axisymmetric, coupled mass, CTRAX3)

• nf043c.dat (parabolic axisymmetric, lumped mass, CQUADX8)

• nf043ct.dat (parabolic axisymmetric, lumped mass, CTRAX6)

• nf043d.dat (parabolic axisymmetric, coupled mass, CQUADX8)

• nf043dt.dat (parabolic axisymmetric, coupled mass, CTRAX6)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Four meshes:

• 60 axisymmetric solid linear quadrilateral (CQUADX4) elements


• 5 axisymmetric solid parabolic quadrilateral (CQUADX8) elements


Boundary Conditions

• Z = 0 at A

Solution Type








Results




NX NastranResult(coupled mass)(Hz)


18.7118.7118.5818.58

18.5418.7218.4318.53

18.5718.7518.5818.60


145.5145.5145.6145.6

138.6160.2136.0139.0

140.2162.0140.6141.0


224.2224.2224.2224.2

224.2224.2224.0224.1

224.2224.3224.2224.2


385.6385.6374.1374.1

361.5417.8353.6369.7

371.5429.3374.0379.3


689.3689.3686.0686.0

643.3687.5633.1680.5

673.8690.3686.0688.5

Note


References


Deep Simply Supported "Solid" Beam

This test is a normal mode dynamic analysis of a deep, simply supported beam meshed with solidelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis , Test 51.





• Skewed coordinate system

• Skewed restraints


Input Files

• nf051a.dat (linear brick)

• nf051b.dat (parabolic brick)

• nf051c.dat (linear pyramid)

• nf051d.dat (parabolic pyramid)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3





Four tests:

• 30 solid linear brick (CHEXA) elements

• 5 solid parabolic brick (CHEXA) elements

• 180 solid linear pyramid (CPYRAM) elements (created by dividing each linear brick elementinto 6 pyramid elements)

• 30 solid parabolic pyramid (CPYRAM) elements (created by dividing each parabolic brick elementinto 6 pyramid elements)

Boundary Conditions

• X′ = Z′ = 0 along AA′

• Z′ = 0 along BB′

• Y′ = 0 at all grid points on the plane Y′ = 2.0 m




Solution Type





Results




NX NastranResult(coupled mass)(Hz)

1 38.20 linear brick

linear pyramid

parabolic brick

parabolicpyramid

42.88

38.82

37.96

41.30

37.85

37.90

38.28

41.50

38.24

38.10


linear pyramid

parabolic brick

parabolicpyramid

93.82

88.45

83.38

89.30

87.12

86.30

83.95

89.60

87.52

86.50


linear pyramid

parabolic brick

parabolicpyramid

170.7

159.4

152.7

163.0

151.8

152.0

157.6

166.0

157.0

155.0


linear pyramid

parabolic brick

parabolicpyramid

286.1

259.2

251.6

269.0

248.5

250.0

264.9

276.0

258.2

255.0


linear pyramid

parabolic brick

parabolicpyramid

318.9

307.9

288.0

303.0

289.6

291.0

298.3

309.0

305.6

300.0




Note


References

NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C.,Selected Benchmarks for Natural Frequency Analysis Test No. 51. Glasgow: NAFEMS, Nov., 1987.

Simply Supported "Solid" Square Plate

This test is a normal mode dynamic analysis of a simply supported square plate meshed with solidelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 52.




• Kinematically incomplete suppressions


Input Files

• nf052l.dat (linear brick)

• nf052b.dat (parabolic brick)



Units

SI

Material Properties

• E = 200E09 N/m2




• ρ = 8000 kg/m3

• ν = 0.3


Four tests:

• 64 solid linear brick (CHEXA) elements

• 16 solid parabolic brick (CHEXA) elements



Boundary Conditions

Z = 0 along the four edges on the plane Z = –0.5 m




Solution Type

SOL 103 normal modes




Results

Mode # ReferenceValue(Hz)


NX NastranResult(lumped mass)(Hz)



linear pyramid

parabolic brick

parabolicpyramid

51.65

44.76

44.04

66.90

43.81

44.70

45.24

68.00

44.16

44.80

5, 6 109.4 linear brick

linear pyramid

parabolic brick

parabolicpyramid

132.7

110.5

106.5

154.0

105.2

109.0

113.7

160.0

107.9

110.0


linear pyramid

parabolic brick

parabolicpyramid

194.4

169.1

155.5

195.0

156.3

166.0

172.3

197.0

163.9

169.0


linear pyramid

parabolic brick

parabolicpyramid

197.2

193.9

193.6

207.0

194.0

194.0

196.8

212.0

193.9

194.0




Mode # ReferenceValue(Hz)


NX NastranResult(lumped mass)(Hz)



linear pyramid

parabolic brick

parabolicpyramid

210.6

206.6

200.1

207.0

193.5

196.0

209.6

212.0

206.6

207.0


linear pyramid

parabolic brick

parabolicpyramid

210.6

206.6

200.1

220.0

193.5

196.0

209.6

223.0

206.6

207.0

Note


References


Simply Supported "Solid" Annular Plate

This test is a normal mode dynamic analysis of a simply supported annular plate meshed with solidelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 53.






• Constraint equations


Input Files

• nf053l.dat (linear brick)

• nf053h.dat (parabolic brick)



Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 0.3


Four tests:

• 60 solid linear brick (CHEXA) elements — α = 5°

• 5 solid parabolic brick (CHEXA) elements — α = 10°






Boundary Conditions

• θ displacement = 0 at all grid points

• Z displacement = 0 at all grid points along AA

• Grid points at same R and Z are constrained to have same z displacement

• One constraint set

Solution Type








Results






linear pyramid

parabolic brick

parabolicpyramid

19.66

18.58

18.57

19.90

18.45

21.30

18.61

19.90

18.58

21.50


linear pyramid

parabolic brick

parabolicpyramid

146.4

140.4

138.8

147.0

135.9

140.0

140.5

148.0

140.3

143.0


linear pyramid

parabolic brick

parabolicpyramid

224.3

224.2

224.2

224.0

223.7

224.0

224.4

224.0

224.2

225.0


linear pyramid

parabolic brick

parabolicpyramid

386.7

374.0

361.8

383.0

351.2

359.0

372.1

390.0

371.9

376.0


linear pyramid

parabolic brick

parabolicpyramid

689.5

686.0

643.8

684.0

624.7

640.0

674.7

690.0

679.6

683.0

References





Cantilevered Solid Beam

This test is a normal mode dynamic analysis of a cantilevered solid beam meshed using solidelements. This document provides the input data and results for NAFEMS Selected Benchmarks forNatural Frequency Analysis, Test 72.


• Highly populated stiffness matrix


Input Files

• nf072a.dat (parabolic bricks – conventional)

• nf072b.dat (parabolic bricks – unconventional)

• nf072c.dat (parabolic pyramids – conventional)

• nf072d.dat (parabolic pyramids – unconventional)

Units

SI

Material Properties

• E = 200E09 N/m2

• ρ = 8000 kg/m3

• ν = 3





Four tests:

• Test 1: solid parabolic brick (CHEXA) elements, conventional grid point numbering

• Test 2: solid parabolic pyramid (CPYRAM) elements (created by dividing each brick element into6 pyramid elements), conventional grid point numbering

• Test 3: solid parabolic brick (CHEXA) elements, unconventional grid point numbering

• Test 4: solid parabolic pyramid (CPYRAM) elements (created by dividing each brick element into6 pyramid elements), unconventional grid point numbering




Boundary Conditions

• X = Y = Z = 0 at all grid points on X = 0 plane

• Y = 0 at grid points on Y = 1 m plane

Solution Type








Results

Mode # Mesh NAFEMS TargetValue (Hz)



1 Test 1

Test 2

Test 3

Test 4

16.01

16.01

15.82

15.90

15.82

15.90

15.99

16.00

15.99

16.002 Test 1

Test 2

Test 3

Test 4

87.23

87.23

83.18

84.30

83.18

84.30

87.09

87.00

87.09

87.003 Test 1

Test 2

Test 3

Test 4

126.0

126.0

125.5

126.0

125.5

126.0

126.0

126.0

126.0

126.04 Test 1

Test 2

Test 3

Test 4

209.6

209.6

193.5

198.0

193.5

198.0

209.1

209.0

209.1

209.05 Test 1

Test 2

Test 3

Test 4

351.1

351.1

310.1

323.0

310.1

323.0

349.9

350.0

349.9

350.06 Test 1

Test 2

Test 3

Test 4

375.8

375.8

364.2

367.0

364.2

367.0

375.8

375.0

375.8

375.0

References




Chapter 6: Verification Test Cases from the SocieteFrancaise des Mecaniciens

6.1 Overview of Verification Test Cases Provided by the SocieteFrancaise des MecaniciensThe purpose of these linear statics test cases is to verify the function of NX Nastran using standardbenchmarks published by SFM (Societe Francaise des Mecaniciens. Paris, France) in Guide devalidation des progiciels de calcul de structures.

Included here are:

• Tests cases on mechanical structures using linear statics analysis, normal mode dynamicsanalysis, and model response.

• Stationary thermal test cases using heat transfer analysis.

• Thermo-mechanical test cases using linear statics analysis.

Results published in Guide de validation des progiciels de calcul de structures are compared withthose computed using NX Nastran.




o Input files

o Units

o Material properties


o Boundary conditions (loads and restraints)

o Solution type

• Results

• Reference

Reference



Chapter 6: Verification Test Cases from the Societe Francaise des Mecaniciens

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures.Paris, Afnor Technique, 1990.

Mechanical Structures — Linear Statics Analysis with Beam or RodElements

Short Beam on Two Articulated Supports

This test is a linear statics analysis of a short, straight beam with plane bending and shear loading.It provides the input data and results for benchmark test SSLL02/89 from Guide de validation desprogiciels de calcul de structures.

• Area = 31E–04 m2

• Inertia = 2810E–08 m4

• Shear area ratio = 2.42


Input Files

ssll02.dat

Units

SI

Material Properties

• E = 2E11 Pa

• ν = 0.3



• 11 grid points

The mesh is shown in the following figure:



Verification Test Cases from the Societe Francaise des Mecaniciens

Boundary Conditions

• Restrain both free ends of the beam in translation DOF.

o Edge load = 1E05 N/m in –Y direction


Solution Type


Results

Result Bench Value NX NastranDisplacement at point B v (m) (Grid point 7) –1.259E–3 –1.249E–3

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SSLL02/89.

Clamped Beams Linked by a Rigid Element

This test is a linear statics analysis of a straight, cantilever beam with plane bending and a rigidelement. It provides the input data and results for benchmark test SSLL05/89 from Guide devalidation des progiciels de calcul de structures.


Input File

ssll05.dat

Units

SI




Material Properties

• E = 2E11 Pa

• I = (4/3)E–08 m4



• 1 rigid element

• 26 grid points


Boundary Conditions

• Points A and C: Clamped

• Point D: Set nodal force = 1000 N in –Y direction


Solution Type


Results

Type Grid point Point BenchValue

NX Nastran

v (m) Disp. Y Grid point 6 B –0.1250 –0.1250v (m) Disp. Y Grid point 3 D –0.1250 –0.1250V force (N) Y Grid point 1 A 500.0 500.0M moment (Nm) Rz Grid point 1 A 500.0 500.0V force (N) Y Grid point 4 C 500.0 500.0





NX Nastran

M moment (Nm) Rz Grid point 4 C 500.0 500.0

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990 Test No. SSLL05/89.

Transverse Bending of a Curved Pipe

This test is a linear statics analysis (three-dimensional problem) of a curved pipe with transversebending and bending-torque loading. It provides the input data and results for benchmark testSSLL07/89 from Guide de validation des progiciels de calcul de structures.

• R = 1 m

• de = 0.02 m

• di = 0.016 m

• A = 1.131E-0–04 m2

• Ix = 4.637E–09 m4


Input Files

• ssll07a.dat linear beam

• ssll07b.dat curved beam

Units

SI




Material Properties

• E = 2E11 Pa

• ν = 0.3


Test 1


• 91 grid points

Test 2

• 90 curved beam (CBEND) elements

• 91 grid points

To obtain the point where θ = 15° with accuracy, use surface mapped meshing on 1/4 of a cylinder.Then mesh a curved edge with the Surface Coating command and undo the mesh on the surface.

The mesh for Test 1 is shown in the following figure:




Boundary Conditions

• Clamp point A.

• Grid point force F = 100 N in Z direction.


Solution Type


Results


TestNumber

NX Nastran

u (m) Disp. Z Grid point 1 B 0.1346 1 0.1346

2 0.1346Mt (Nm)* Grid point 1 θ = 15° 74.12 1 76.67

2 77.51Mf (Nm) –96.59 1 –96.37

2 –95.70

Mf = bending moment

Mt = torsional moment

*See "Post Processing" below.




Post Processing

Linear Beam (CBAR) Elements

List beam forces on element 167, second end:

• Mf = torque

• Mt = bending moment

Curved Beam (CBEND) Elements

List beam forces on element 166, second end:

• Mf = torque

• Mt = bending moment

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990.Test No. SSLL07/89..

Plane Bending Load on a Thin Arch

This test is a linear statics analysis (plane problem) of a thin arc with plane bending. It provides theinput data and results for benchmark test SSLL08/89 from Guide de validation des progiciels decalcul de structures.

• R = 1 m

• de = 0.02 m

• di = 0.016 m

• A = 1.131E–04 m2

• Ix 4.637E–09 m4





Input File

ssll08.dat

Units

SI

Material Properties

• E = 2E11 Pa

• ν = 0.3



• 11 grid points




Boundary Conditions

• Point A: Articulated Z

• Point B: Sets Y and Z displacement to 0

• Force = 100N in –Y direction


Solution Type


Results

Type Grid Point Point Bench Value NX NastranRz (rad) 2 A –3.077E–2 –3.110E–2Rz (rad) 1 B 3.077E–2 3.110E–2Y (m) 7 C -1.921E–2 –1.934E–2X (m) 1 B 5.391E-2 5.374E–2

References


Grid Point Load on an Articulated CONROD Truss

This test is a linear statics analysis of a plane truss with an articulated rod. It provides the input dataand results for benchmark test SSLL11/89 from Guide de validation des progiciels de calcul destructures.





Input File

ssll11.dat

Units

SI

Material Properties

• E = 1.962E11 Pa





• 4 rod (CONROD) elements

• 4 grid points


Element Length (m) Area (m2)AC 2.000E–4

CB 2.000E–4

CD 1.000E–4

BD 1.000E–4

Boundary Conditions

• Point A and B: Articulated

• Point D: Set Nodal force = 9.81 E3 N in –Y direction


Solution Type





Results

Type Grid Point Point Bench Value NX NastranX (m) 18.00 C 0.2652E–3 0.2652E–3Y (m) 18.00 C 0.08839E–3 0.08839E–3X (m) 2.000 D 3.479E–3 3.479E–3Y (m) 2.000 D –5.601E–3 –5.600E–3

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures.(Paris, Afnor Technique, 1990..) Test No. SSLL11/89.

Articulated Plane Truss

This test is a linear statics analysis of a straight cantilever beam with plane bending andtension-compression. It provides the input data and results for benchmark test SSLL14/89 from Guidede validation des progiciels de calcul de structures.

• I1 = 5E–04 m4

• I2 = 2.5E–04 m4





Input Files

• ssll14a.dat (4 elements)

• ssll14b.dat (10 elements)

Units

SI

Material Properties

• E = 2.1E11 Pa


Test 1


• 5 grid points

Test 2


• 11 grid points

The mesh for Test 2 is shown in the following figure:




Boundary Conditions

• Point A and B: Articulate

• Set forces and moments to the following numeric values:

o p = –3,000 N/m

o F1 = –20,000 N

o F2 = –10,000 N

o M = –100,000 Nm


Solution Type


Results

Type Grid Point Point Bench Value TestNumber

NX Nastran

Vertical reaction(N)

1.000 A 3.150E4 1

2

3.150E4

3.320E4Hortizontalreaction (N)

1.000 A 2.024E4 1

2

1.920E4

2.061E4VerticalDisplacement (m)

8.000 C 0.03072 1

2

–0.02100

–0.03161

Note

NX Nastran takes shear effect into account.




References


Beam on an Elastic Foundation

This test is a linear statics analysis (plane problem) of a straight beam with plane bending and anelastic support. It provides the input data and results for benchmark test SSLL16/89 from Guide devalidation des progiciels de calcul de structures.


Input File

ssll16.dat

Units

SI

Material Properties

• E = 2.1E11 Pa

• K = 8.4E05 N/m2

• Each spring stiffness is set to: K * L/(number of spring elements).






• 49 spring (CBUSH) elements

• 51 grid points





Boundary Conditions

• Point A and B: Articulated

• Set forces and moments to the following numeric values:

–F = –10000 N

–p = –5000 N/m

–M = 15000 Nm.


Solution Type


Results

Type Point Bench Value NX NastranRotation(rad) Rz A —0.003050 –0.003034Vertical Reaction force (N) 1.167E4 1.158E4Vertical Disp. (m) D –0.4233E–2 –0.4216E–2




Type Point Bench Value NX NastranM moment (Nm)* 3.384E4 3.369E4

*List beam forces on element 26, first end, z bending moment.

References


Mechanical Structures — Linear Statics Analysis with Shell Elements

Plane Shear and Bending Load on a Plate

This test is a linear statics analysis (plane problem) of a plate with plane bending. It provides theinput data and results for benchmark test SSLP01/89 from Guide de validation des progiciels decalcul de structures.

• Thickness = 1 mm


Input File

sslp01.dat

Units

SI

Material Properties

• E = 3E10 Pa

• ν = 0.25





• 100 linear quadrilateral thin shell (CQUAD4) elements

• 126 grid points


Boundary Conditions

• Clamped Plate

• Set a shear force with parabolic distribution on width and constant distribution on thickness.

• Resultant force: p = 40 N.


Solution Type


Results

Type Grid point # Location Bench Value NX NastranY (mm) Grid point 3 (L,y) 0.3413 0.3408

Displacement is shown in the following figure:




References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990 Test No. SSLP01/89.

Infinite Plate with a Circular Hole

This test is a linear statics analysis (plane problem) of a plate with tension-compression and amembrane effect. It provides the input data and results for benchmark test SSLP02/89 from Guide devalidation des progiciels de calcul de structures.





Input File

sslp02.dat

Units

SI

Material Properties

• E = 3E10 Pa

• ν = 0.25






• 121 grid points

The plate is meshed using the biasing option.


Boundary Conditions

• u (0,y) = 0, Ry (y) = 0, Rz (y) = 0, (z = 0, all grid points)

• ν (x,0) = 0, Rx (x) = 0, Rz (x) = 0

• Tension force P = 2.5 N/mm**2 (in plane force of 2500 N/m)





Solution Type


Results

Type Point Bench Value NX Nastranσθθ (a, 0) 7.500E7 7.528E7σθθ (a, π/4) 2.500E7 2.511E7σθθ (a, π/2) –2.500E7 –2.452E7

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SSLP02/89.

Uniformly Distributed Load on a Circular Plate

This test is a linear statics analysis (three-dimensional problem) of a circular plate fixed at the edgewith transverse bending and a uniform load. It provides the input data and results for benchmark testSSLS03/89 from Guide de validation des progiciels de calcul de structures.


Input Files

• ssls03a.dat linear quadrilateral

• ssls03b.dat linear triangle

Units

SI




Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3


Test 1


• 50 grid points

Test 2

• 53 linear triangular thin shell (CTRIA3) elements

• 38 grid points

Meshing is only done on 1/4 of the plate.

The meshes are shown in the following figure:




Boundary Conditions

• Clamp free edges.

• Uniform pressure p = –1000 Pa.

• Symmetric conditions are applied to the sides.


Solution Type


Results

Result Grid Point Point Bench Value Test Number NX NastranZ 1.000 Center O –0.006500 1 –0.006600w (m) 1.000 2 –0.006500

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SSLS03/89.

Torque Loading on a Square Tube

This test is a linear statics analysis (three-dimensional problem) of a thin-walled tube loaded in torsionby pure shear at the free end. It provides the input data and results for benchmark test SSLS05/89from Guide de validation des progiciels de calcul de structures.





Input File

ssls05.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• = 0.3


• 160 CQUAD4 elements

• 219 grid points





Boundary Conditions

• Plane X = 0

• Clamped beam

• Apply a torque equal to 10 Nm on the free end.


Solution Type


Results

Result Grid Point Bench Value NX NastranDisp. Y (m) 193.0 –6.170E–7 .6.170E–7Disp. Rx (rad) 1.230E–5 1.230E–5Stress XY Shear (Pa) –11.00E4 –11.00E4Disp. Y (m) 208.0 –9.870E–7 –9.870E–7Disp. Rx (rad) 1.970E–5 1.970E–5Stress XY Shear (Pa) –11.00E4 –11.00E4

Results are post-processed using the Shell surface: Bottom option.

References


Cylindrical Shell with Internal Pressure

This test is a linear statics analysis of a thin cylinder loaded by internal pressure. It provides theinput data and results for benchmark test SSLS06/89 from Guide de validation des progiciels decalcul de structures.





Input Files

• ssls06a.dat

• ssls06b.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3






Test 1


• 121 grid points

Test 2

• 400 liinear quadrilateral thin shell (CQUAD4) elements

• 441 grid points




Boundary Conditions

• Free conditions:

To set free boundary conditions, use symmetry about XZ, XY, and YZ planes.

• Internal pressure = 10000 Pa.


Solution Type


Results

Type Point Bench Value TestNumber

NX Nastran

σ11(Pa) All 0 1 1.7202 4.960

σ22(Pa) 5.000E5 1 4.950E52 4.990E5

ΔR(m) 2.380E–6 1 2.370E–62 2.380E–6

ΔL(m) –1.430E–6 1 –1.420E–62 –1.430E–6

All results are averages.




Post Processing

• σ11 is the stress of z at grid point 11 (test 1) and grid point 21 (test 2)

• σ22 is the stress of x at grid point 111 (test 1) and grid point 421 (test 2)

• ΔR(m) is the displacement of x at grid point 121 (test 1) and grid point 441 (test 2)

• ΔL(m) is the displacement of z at grid point 121 (test 1) and grid point 441 (test 2)

References


Uniform Axial Load on a Thin Wall Cylinder

This test is a linear static analysis of a thin cylinder loaded axially. It provides the input data andresults for benchmark test SSLS07/89 from Guide de validation des progiciels de calcul de structures.


Input Files

• ssls07a.dat – parabolic quadrilateral, thin shell

• ssls07b.dat – parabolic triangle, thin shell

Units

SI




Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3


Test 1

• 200 parabolic quadrilateral thin shell (CQUAD8) elements

• 661 grid points

Test 2

• 400 parabolic triangular thin shell (CTRIA6) elements





Boundary Conditions

• Axial displacement = 0 in. X = 0 section

• Uniform axial load q = 10000 N/m


Solution Type

SOL 101 — Linear Sstatics

Results

Type Point Bench Value Test Number NX Nastranσ11(Pa) Any 5.000E5 1 5.000E5

2 5.790E5σ22(Pa) Any 0 1 0

2 3.080E4ΔL(m) Any 9.520E–6 1 9.520E–6

2 9.560E–6ΔR (m) Any –7.140E–7 1 –7.140E-7

2 –7.330E–7

All results are averages.

Post Processing

• σ11 is the stress of z at grid point 641 in coordinate system 2.




• σ22 is the stress of y at grid point 641 in coordinate system 2.

• ΔR is the displacement of x at grid point 641 in coordinate system 2.

• ΔL is the displacement of z at grid point 641 in coordinate system 2.

References


Hydrostatic Pressure on a Thin Wall Cylinder

This test is a linear statics analysis of a thin cylinder loaded by hydrostatic pressure. It provides theinput data and results for benchmark test SSLS08/89 from Guide de validation des progiciels decalcul de structures.


Input File

ssls08.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3






• 661 grid points





Boundary Conditions

• Restrain the grid points on side A (from grid point 21 to grid point 661) in the X translation andthe Y and Z rotations.

• Restrain the grid points on side B (from grid point 1 to grid point 641) in the Y translation and Xand Z rotations.

• Internal pressure p = p0 * Z/L with p0 = 20000 Pa.


Solution Type


Results

Type Grid Point Point Bench Value NX Nastranσ11(Pa) 321.0 Any 0 8.800E3L/2σ22 (Pa) 321.0 x = L/2 5.000E5 4.970E5ΔR (m) 321.0 x = L/2 2.380E–6 2.380E–6ΔL (m) 1.000 x = L –2.860E–6 2.860E–6Ψ (rad) 321.0 1.190E–6 1.190E–6

Ψ represents the rotation of a generator.

Post Processing

• σ11is the stress of z at grid point 321 in coordinate system 2




• σ22 is the stress of y at grid point 321 in coordinate system 2

• ΔR is the displacement of x at grid point 321 in coordinate system 2

• ΔL is the displacement of z at grid point 1 in coordinate system 2

• Ψ is the rotation of y at grid point 321 in coordinate system 2

References


Pinched Cylindrical Shell

This test is a linear statics analysis of a cylindrical shell with grid point forces, F, pinching as shown.It provides the input data and results for benchmark test SSLS20/89 from Guide de validation desprogiciels de calcul de structures.


Input Files

• ssls20a.dat linear triangle thin shells

• ssls20b.dat linear quadrilateral thin shells

Units

SI




Material Properties

• E = 10.5 x 106 Pa

• ν = 0.3125


Test 1


• 173 grid points

Test 2


• 165 grid points





Boundary Conditions

• Free conditions

To set free boundary conditions, use symmetry about XY, XZ, and YZ planes.

• Grid point forces Fy = –25 N at point D


Solution Type


Results

Type Point Bench Value Test Number NX NastranDisp. Y (Grid point 3) ν(m) D –113.9E-3 1 –114.4E–3Disp. Y (Grid point 3) 2 –113.3E–3

Post Processing

• ν(m) is the displacement of y at grid point 3 (quadrilateral).

References


Spherical Shell with a Hole

This test is a linear statics analysis of a spherical shell with a hole with grid point forces. It providesthe input data and results for benchmark test SSLS21/89 from Guide de validation des progiciels decalcul de structures.





Input Files

• ssls21a.dat – linear quadrilateral thing shells

• ssls21b.dat – linear triangle thin shells

• ssls21c – parabolic quadrilateral thin shells

Units

SI

Material Properties

• E = 6.285 x 107 Pa

• ν = 0.3





Test 1


• 121 grid points

Test 2


• 121 grid points

Test 3


• 441 grid points





Boundary Conditions

• Free conditions

To set free boundary conditions, use symmetry about XY and YZ planes.

• Grid point forces F = 2 Newtons

Due to the symmetric boundary conditions, only half of the load is applied.


Solution Type


Results

Result Point BenchValue

TestNumber

NX Nastran

u (m) grid point 111 A(R,0,0) 9.400E–2 1 102.0E–3Grid point 111 2 102.1E–3Grid point 421 3 100.9E–3

References


Bending Load on a Cylindrical Shell

This test is a linear statics analysis of a cylindrical shell with bending and membrane effect. Itprovides the input data and results for benchmark test SSLS23/89 from Guide de validation desprogiciels de calcul de structures.





Input Files

• ssls23a.dat (Test 1, linear)

• ssls23b.dat (Test 2, parabolic)

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3





Test 1


• 78 grid points

Test 2


• 215 grid points


Boundary Conditions

• AB side: Clamped in local system coordinates.

• AD and BC sides: Restrain Z translation, θx and θy.

• DC side: Set bending moment CZ to 1000 Nm/m. Set in plane force to 0.6E6 N/m.

• ABCD surface: Set internal pressure to 0.6E06 N/m**2.

• AD and DC sides are restrained in the global coordinate system.


Solution Type





Results

Use coordinate system 3 (the cylindrical coordinate system) to display the results.

Results are post-processed using the Shell surface middle option.

Result Point Bench Value Test Number NX NastranGrid point 35 E 60.00 MPa 1 60.70Grid point 93 2 59.60

References


Uniformly Distributed Load on a Simply-Supported Rectangular Plate

This test is a linear statics analysis of a plate with pressure loading and simple supports. It providesthe input data and results for benchmark test SSLS24/89 from Guide de validation des progiciels decalcul de structures.


Input Files

• ssls24a.dat (Test 1, coarse mesh)

• ssls24b.dat (Test 2, fine mesh)

• ssls24c.dat (Test 3, very fine mesh)

Units

SI




Material Properties

• E = 1.0 x 107 Pa

• ν = 0.3


Test 1 — a/b = 1


• 121 grid points

Test 2 — a/b = 2


• 231 grid points

Test 3 — a/b = 5


• 561 grid points





Boundary Conditions

Restraints

• All edges: w = 0

• One corner fixed

Loads

• Set pressure = 1 N/m**2 in the –Z direction


Solution Type


Results

Result a/b Parameters Bench Value Test Number NX Nastran61z direction 1.000 1.000α 0.004440 1 0.004500116z direction 2.000 2.000α 0.01110 2 0.01110281z direction 5.000 5.000α 0.01417 3 0.0140661x component topsurface

1.000 1.000β 2874. 1 2867.

116x component topsurface

2.000 2.000β 6102. 2 6034.




Result a/b Parameters Bench Value Test Number NX Nastran281x component topsurface

5.000 5.000β 7476. 3 7331.

Where:

q = distributed load

b = dimension

t = thickness

E = elastic modules

β values of reference from the Guide de Validation are incorrect. The correct values are extractedfrom Formulas for Stress and Strain (Roark/Young).

Note

Note that the shell top surface corresponds to the side of the plate with negative globalZ coordinates.

References


Uniformly Distributed Load on a Simply-Supported Rhomboid Plate

This test is a linear statics analysis (three-dimensional problem) of a plate with pressure andtransverse bending. It provides the input data and results for benchmark test SSLS25/89 from Guidede validation des progiciels de calcul de structures.


• b = 1.0 m

• a = 2.0 m





Input Files

• ssls25a.dat (Test 1)

• ssls25b.dat (Test 2)

Units

SI

Material Properties

• E = 36.0 x 106 Pa

• ν = 0.3


• a/b = 2

• Linear quadratic thin shell (CQUAD4) elements

Test 1

• θ = 30°

Test 2

• θ = 45°





Boundary Conditions

• All edges: w = 0, one corner fixed

• Pressure = 1 N/m2 in the –Z direction


Solution Type


Results

Parameter Test Case Bench Value NX Nastranα Test 1

ssls25a

z displacement

–3.277E–3 m

116z displacement

–2.963E–3 mβ Y stress

–5.700E3 N/m2

116y stress

–5.831E3 N/m2α Test 2

ssls25b

z displacement

–3.000E-3 m

116z displacement

–2.720E–3 mβ Y stress

–5.390E3 N/m2

116Y stress

–5.441E3 N/m2

Where:

q = distributed load

b = dimension




t = thickness

E = elastic modulus

Values of reference from the Guide de validation are incorrect. The correct values are extracted fromFormulas for Stress and Strain (Roark/Young), table 26, case number 14a.

References


Shear Loading on a Plate

This test is a linear statics analysis of a thin plate with torque and shear loading. It provides theinput data and results for benchmark test SSLS27/89 from Guide de validation des progiciels decalcul de structures.


Input Files

• ssls27a.dat (Test 1, Mindlin)

• ssls27b.dat (Test 2, Kirchoff)

• ssls27c.dat (Test 3, Mindlin)

Units

SI

Material Properties

• E = 1.0 x 107 Pa

• ν = 0.25





Test 1 — Mindlin


• 14 grid points

Test 2 — Kirchhoff


• 14 grid points

Test 3 — Mindlin


• 75 grid points


All tests are executed with mapped meshing

Boundary Conditions

• Clamp AD side

• Point B: grid point force Fz = –1N

• Point C: grid point force –Fz = 1N


Solution Type





Results at Location C

Displacement at Gridpoint

Bench Value Test Number NX Nastran

14.00 3.537E–2 1 3.585E–214.00 3.537E–2 2 3.573E–275.00 3.537E–2 3 3.603E–2

References


Mechanical Structures — Linear Statics Analysis with Solid Elements

Solid Cylinder in Pure Tension

This test is a linear statics analysis of a solid cylinder with tension-compression. It provides theinput data and results for benchmark test SSLV01/89 from Guide de validation des progiciels decalcul de structures.





Input Files

• sslv01a.dat (Test 1)

• sslv01b.dat (Test 2)

• sslv01c.dat (Test 3)

• sslv01d.dat (Test 4)

• sslv01e.dat (Test 5)

• sslv01f.dat (Test 6)

Units

SI

Material Properties

• E = 2.0 x 1011 Pa

• ν = 0.30





Test 1

• 155 parabolic tetrahedron (CTETRA) elements

• 342 grid points

Test 2

• 144 linear brick (CHEXA) elements & 48 linear solid wedge (CPENTA) elements

• 307 grid points

Test 3 (Results for this test will be provided in the NX Nastran 7 Verification Manual)

• 48 linear quadrilateral axisymmetric solid elements

• 65 grid points


• 96 linear triangular axisymmetric solid elements

• 65 grid points


• 18 parabolic quadrilateral axisymmetric solid elements

• 95 grid points

Test 6

• 864 linear pyramid (CPYRAM) elements created by dividing each brick element in test 2 into 6pyramid elements. 48 linear wedge (CPENTA) elements remain.




Boundary Conditions

• Uniaxial deformation of the cylinder section

• Set uniformly distributed force –F/A on the free end in the Z direction

• F/A = 100 MPa


Solution Type


Results

linear statics

* axisymmetric data will be provided in version 7

Point GridPoint

Displacement BenchValue

TestNumber

NX Nastran

A & C 6 u (m) 1.500E–3 1 1.500E–3A & C 279 2 1.500E–3A & C 1 3 *A & C 4 4 *A & C 1 5 *




Point GridPoint


TestNumber

NX Nastran

A & C 279 6 1.500E–3B 4 u (m) 1.500E–3 1 1.500E–3B 307 2 1.500E–3B 53 3 *B 3 4 *B 39 5 *B 307 6 1.500E–3D 37 u (m) 1.000E-3 1 1.000E–3D 189 2 1.000E–3D 5 3 *D 25 4 *D 7 5 *D 189 6 1.000E–3E 41 u (m) 0.5000E-3 1 0.500E–3E 99 2 0.500E–3E 9 3 *E 29 4 *E 13 5 *E 99 6 0.500E–3A & C 6 w (m) –0.1500E–3 1 –0.150E–3A & C 279 2 –0.150E–3A & C 1 3 *A & C 4 4 *A & C 1 5 *A & C 279 6 –0.1500E–3D 37 w (m) –0.1500E-3 1 –0.1500E–3D 189 2 –0.1500E–3D 5 3 *D 25 4 *D 7 5 *D 189 6 –0.1500E–3E 41 w (m) –0.1500E–3 1 –0.1500E–3E 99 2 –0.1500E–3E 9 3 *E 29 4 *E 13 5 *




Point GridPoint


TestNumber

NX Nastran

E 99 6 –0.1500E–3

Post Processing

To view the results for Test 1 and Test 2, use coordinate system 2 (cylindrical). u is the radialdisplacement and w is the axial displacement.

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SSLV01/89.

Internal Pressure on a Thick-Walled Spherical Container

This test is a linear statics analysis of a thick sphere with internal pressure. It provides the input dataand results for benchmark test SSLV03/89 from Guide de validation des progiciels de calcul destructures.


Input Files







Units

SI




Material Properties

• E = 2 x 105 Pa

• ν = 0.3


Test 1

• 1600 linear brick (CHEXA) elements & linear solid wedge (CPENTA) elements

• 1898 grid points

Test 2

• 200 parabolic brick (CHEXA) elements & 50 solid wedge (CPENTA) elements




• 451 grid points




Test 5

• Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6pyramid elements. Wedge (CPENTA) elements remain.

Test 6

• Parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 2 into 6pyramid elements. Wedge (CPENTA) elements remain.




The meshes from these tests are shown in the following figure:




Boundary Conditions

• The equivalent of the center of the sphere being fixed is modeled via symmetric boundaryconditions.

• Uniform radial pressure = 100 MPa.


Solution Type


Results

* axisymmetric data will be provided in version 7

Point GridPoint

DisplacementStress

BenchValue

Test Number NX Nastran

r=1 m 1 σrr (MPa) –100.0 1 –90.151 2 –97.29451 3 *451 4 *1 5 –90.841 6 -103.81 σθ (MPa) 71.43 1 72.09




Point GridPoint

DisplacementStress

BenchValue


1 2 77.23451 3 *451 4 *1 5 72.061 6 73.301 u (m) 0.4000E–3 1 0.4000E–31 2 0.4000E–3451 3 *451 4 *1 5 0.3991E–31 6 0.4006E–3




Point GridPoint

DisplacementStress

BenchValue


r=2 m 1826 σrr (MPa) 0 1 –0.02802221 2 0.2240411 3 *411 4 *1826 5 –0.25302221 6 –0.52591826 σθ (MPa) 21.43 1 21.182221 2 21.18411 3 *411 4 *1826 5 21.402221 6 21.741826 u (m) 1.500E–4 1 1.500E–42221 2 1.500E–4411 3 *411 4 *1826 5 1.506E–42221 6 1.499E–4

All stress results are averaged. Use the spherical coordinate system for the stress results.

References


Internal Pressure on a Thick-Walled Infinite Cylinder

This test is a linear statics analysis of a thick cylinder with internal pressure. It provides the inputdata and results for benchmark test SSLV04/89 from Guide de validation des progiciels de calcul destructures.





Input Files







Units

SI

Material Properties

• E = 2 x 105 mPa

• ν = 0.3


Test 1

• 400 linear brick (CHEXA) elements

• 902 grid points

Test 2

• 240 parabolic brick (CHEXA) elements





Test 3


• 656 grid points

Test 4



Test 5

• Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6pyramid elements.

Test 6

• Parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 2 into6 pyramid elements.

The brick meshes are shown in the following figure:




Boundary Conditions

• Unlimited cylinder

• Internal pressure p = 60 MPa


Solution Type


Results

All results are averaged.

Test Case GridPoint

Displacement / Stress Bench Value NX Nastran

sslv04a 411 σr –60.00 (MPa) –57.00sslv04b 977 –60.00sslv04c 616 *sslv04d 1831 *sslv04e 411 –57.30sslv04f 977 –60.74sslv04a 411 σθ 100.0 (MPa) 99.70sslv04b 977 102.0sslv04c 616 *sslv04d 1831 *sslv04e 411 99.68sslv04f 977 100.9sslv04a 411 τmax 80.00 (MPa) 79.34sslv04b 977 81.00sslv04c 616 *sslv04d 1831 *




Test Case GridPoint

Displacement / Stress Bench Value NX Nastran

sslv04e 411 80.82sslv04f 977 80.82sslv04a 411 ur 59.00E–6 (m) 59.00E–6sslv04b 977 59.00E–6sslv04c 616 *sslv04d 1831 *sslv04e 411 58.85E–6sslv04f 977 59.00E–6sslv04a 451 σr 0 (MPa) –0.006500sslv04b –0.04480sslv04c *sslv04d *sslv04e –0.1563sslv04f –0.1900sslv04a σθ 40.00 (MPa) 39.66sslv04b 40.39

sslv04c *sslv04d *sslv04e 39.84sslv04f 40.16

sslv04a τmax 20.00 (MPa) 20.08sslv04b 20.17sslv04c 20.07sslv04d 19.99sslv04e 20.10sslv04f 20.17sslv04a ur 40.00E–6 (m) 40.00E–6sslv04b 40.00E–6sslv04c *sslv04d *sslv04e 39.93E–6sslv04f 40.00E–6




References


Prismatic Rod in Pure Bending

This test is a linear statics analysis of a solid rod with bending. It provides the input data and resultsfor benchmark test SSLV08/89 from Guide de validation des progiciels de calcul de structures.


Input Files







Units

SI




Material Properties

• E = 2 x 105 MPa

• ν = 0.3





Test 1

• 198 linear solid tetrahedral (CTETRA) elements

• 76 grid points

Test 2

• 198 parabolic solid tetrahedral (CTETRA) elements

• 409 grid points

Test 3


• 117 grid points

Test 4 — Mapped meshing

• 48 parabolic brick (CHEXA) elements

• 381 grid points

Test 5

• 288 linear pyramid (CPYRAM) elements created by dividing each brick element in test 3 into6 pyramid elements.

Test 6

• 288 parabolic pyramid (CPYRAM) elements created by dividing each brick element in test 4 into6 pyramid elements.





Boundary Conditions

• Clamp Point B.

• Other points of B section: Set Z-displacement to 0. NOTE: In these tests some grid points ofsection B are also restrained in the x direction about the x-axis at the free end of the rod.

• Set moment Mx equal to (4/3)E+7 N.m


Solution Type


Results

Test # Point GridPoint

DisplacementStress

Bench Value NX Nastran

1 F or G 5 σzz –10.00E6 (Pa) –4.268E62 5 –10.03E63 75 –10.00E64 245 –9.995E65 75 –7.929E66 245 –9.992E61 A 26 uA 4.000E–4 (m) 2.964E–42 90 4.000E–43 77 4.000E–44 251 4.000E–4




Test # Point GridPoint

DisplacementStress

Bench Value NX Nastran

5 77 3.443E–46 251 4.000E–41 H 19 wB 2.000E–4 (m) 2.000E–42 40 2.000E–43 76 2.000E–44 249 2.000E–45 76 1.721E–46 249 2.000E–41 F or G 5 vF = -vG 0.1500E-4 (m) 0.07450E–42 5 0.1508E–43 75 0.1500E–44 245 0.1503E–45 75 0.1005E–46 245 0.1503E–41 D or E 8 vD = -vE -0.1500E-4 (m) –6.262E–42 8 –0.1505E–43 73 –0.1500E–44 241 –0.1503E–45 73 –0.1005E–46 241 –0.1503E–4

References


Thick Plate Clamped at Edges

This test is a linear statics analysis of a thick plate with pressure and transverse bending. It providesthe input data and results for benchmark test SSLV09/89 from Guide de validation des progiciels decalcul de structures.





Input Files




Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3





Test 1

• 25 parabolic linear brick (CHEXA) elements

• 228 grid points

• λ =10, 20, 50, 75, 100

Test 2


• 36 grid points

• λ =10, 20, 50, 75, 100

Test 3

• 150 linear pyramid solid (CPYRAM) elements created by dividing each brick element in test1 into 6 pyramid elements

Test 2 is done using CQUAD4 elements with the thicknesses specified in the physical property table.





Boundary Conditions

• AB and AD sides: clamped

• BC and DC sides: symmetry

• Load case 1:

Pressure p = 1E06 Pascals in –Z direction

• Load case 2: Point C

Grid Point force F = 1E06 N in –Z direction


Solution Type

SOL 101 Linear statics




Results

Test Case 1 (z displacement at location C)

PartName

Load Case Grid Point Analytical Reference FEM NX Nastran

10 Pressure 242 –0.6552E-4 –0.7620E–4 –0.7379E–4

Force 242 –0.2915E-3 –0.4300E–3 –0.3684E–3

20 Pressure 1242 –0.5242E-3 –0.5383E–3 –0.5266E–3

Force 1242 –0.2332E–2 –0.2535E–2 –0.2456E–2

50 Pressure 2242 –0.8190E–2 –0.8029E–2 –0.7935E–2

Force 2242 –0.3643E–1 –0.3574E–1 –0.3602E–1

75 Pressure 3242 –0.2764E–1 –0.2690E–1 –0.2666E-1

Force 3242 –0.1230 –0.1184 –0.1206

100 Pressure 4242 –0.6552E–1 –0.6339E–1 –0.6305E–1

Force 4242 –0.2915 –0.2779 –0.2849


PartName


10 Pressure 1 –0.6552E–4 –0.7866E–4 –0.8131E–4

Force 1 –0.2915E–3 –0.4109E–3 –0.4050E–3

20 Pressure 36 –0.5242E–3 –0.5557E–3 –0.5775E–3

Force 36 –0.2332E–2 –0.2595E–2 –0.2668E–2

50 Pressure 36 –0.8190E–2 –0.8348E–2 –0.8669E–2

Force 36 –0.3643E–1 –0.3745E–1 –0.3878E–1

75 Pressure 36 –0.2764E–1 –0.2805E–1 –0.2906E–1

Force 36 –0.1230 –0.1253 –0.1292

100 Pressure 36 –0.6552E–1 –0.6639E–1 –0.6864E–1

Force 36 –0.2915 -0.2958 –0.3042


PartName


10 Pressure 242 –0.6552E-4 –0.7620E–4 –0.7491E–4

Force 242 –0.2915E-3 –0.4300E–3 –0.3736E–3

20 Pressure 1242 –0.5242E-3 –0.5383E–3 –0.5342E–3

Force 1242 –0.2332E–2 –0.2535E–2 –0.2458E–2

50 Pressure 2242 –0.8190E–2 –0.8029E–2 –0.7875E–2

Force 2242 –0.3643E–1 –0.3574E–1 –0.3470E–1

75 Pressure 3242 –0.2764E–1 –0.2690E–1 –0.2605E-1

Force 3242 –0.1230 –0.1184 –0.1135




PartName


100 Pressure 4242 –0.6552E–1 –0.6339E–1 –0.6068E–1

Force 4242 –0.2915 –0.2779 –0.2627

References


Mechanical Structures — Normal Mode Dynamics Analysis

Lumped Mass-Spring System

This test is a normal mode dynamics analysis of an elastic link with lumped mass. It provides theinput data and results for benchmark test SDLD02/89 from Guide de validation des progiciels decalcul de structures.


Input File

sdld02.dat

Units

SI

Material Properties

Spring constant





• 8 lumped mass (CONM2) elements

• 9 spring (CBUSH) elements

• 8 grid points


Boundary Conditions

• Clamp points A and B

• Other points:

ν = 0 ; θ = 0


Solution Type

SOL 103 — Normal Modes




Results

Frequency Results (Hz)

Normal Mode Bench Value NX Nastran1 5.527 5.5272 10.89 10.893 15.92 15.924 20.46 20.465 24.38 24.386 27.57 27.577 29.91 29.918 31.35 31.35

Mode Shapes Results

The mode shapes results are exact. The multiplication coefficient is 3.162.

Normal Mode Point Bench Value NX Nastran1 P1 0.1612 0.05100

P2 0.3030 0.09580P3 0.4082 0.1291P4 0.4642 0.1468P5 0.4642 0.1468P6 0.4082 0.1291P7 0.3030 0.09580P8 0.1612 0.05100

8 P1 0.1612 0.05100P2 –0.3030 –0.09580P3 0.4082 0.1291P4 –0.4642 –0.1468P5 0.4642 0.1468P6 –0.4082 –0.1291P7 0.3030 0.09580P8 –0.1612 –0.05100

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLD02/89, p. 178.




Short Beam on Simple Supports

This test is a modal analysis of a straight short beam with simple supports both inline and offset. Itprovides the input data and results for benchmark test SDLL01/89 from Guide de validation desprogiciels de calcul de structures.


Input Files

• sdll01a.dat (Test 1)

• sdll01b.dat (Test 2)

Units

SI

Material Properties

• E = 2 x 101111 Pa

• ν = 0.3

• ρ = 7800 kg/m3






• 11 grid points





Boundary Conditions

Problem 1

• Point A (grid point 1): Constrain in all directions, except the Z rotation.

• Point B (grid point 2): Constrain in the Y and Z translations and X and Y rotations.

• All other grid points (3-11): Constrain in the Z translation and X and Y rotations.

• No load case.

Problem 2

• Point C (grid point 1): Constrain in all directions, except the Z rotation.

• Point D (grid point 2): Constrain in the Y and Z translations and X and Y rotations.

• All other grid points (3-11): Constrain in the Z translation and X and Y rotations.

• No load case.


Solution Type





Results

Problem 1: Frequency results (Hz)

Normal Mode Bench Value NX NastranBending 1 431.6 437.2Tension 1 1266. 1265.Bending 2 1498. 1539.Bending 3 2871. 2925.Tension 2 3798. 3763.Bending 4 4378. 4328.


Mode Number Bench Value NX Nastran1 392.8 398.52 902.2 927.33 1592. 1666.4 2629. 2815.5 3126. 3266.

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLL01/89.

Axial Loading on a Rod

This test is a modal analysis of a simply-supported beam with stress stiffening. It provides the inputdata and results for benchmark test SDLL05/89 from Guide de validation des progiciels de calcul destructures.


Input Files

• sdll05a.dat

• sdll05b.dat




Units

SI

Material Properties

• E = 2 x 1011 Pa

• ρ = 7800 kg/m3



• 11 grid points





Boundary Conditions

• Points A: u = v = 0

• Points B: v = 0

• Load case 2 (grid point 2): Fx = 1E05N in –X direction

• Stress stiffening on


Solution Type


Results

Frequency results (Hz)

Load Case Normal Mode Bench Value NX Nastran1 Bending 1 28.70 28.68

Bending 2 114.8 114.42 Bending 1 22.43 22.40

Bending 2 109.1 108.7

References


Cantilever Beam with a Variable Rectangular Section

This test is a modal analysis of a straight cantilever beam with a variable section. It provides theinput data and results for benchmark test SDLL09/89 from Guide de validation des progiciels decalcul de structures.





Input Files

• sdll09a.dat

• sdll09b.dat

Units

SI

Material Properties

• E = 2 x 1011 Pa

• ρ = 7800 kg/m3


• 10 tapered beam (CBEAM) elements

• 11 grid points





Boundary Conditions

• Clamp point A

• No load case


Solution Type


Results


β Normal Mode Bench Value NX Nastran4 1 54.18 54.24

2 171.9 172.43 384.4 384.94 697.2 695.45 1112. 1104.

5 1 56.55 56.592 175.8 176.33 389.0 389.54 702.4 700.65 1118. 1109.

References


Thin Circular Ring

This test is a modal analysis of a thin curved beam. It provides the input data and results forbenchmark test SDLL11/89 from Guide de validation des progiciels de calcul de structures.





Input File

sdll11.dat

Units

SI

Material Properties

• E = 7.2 x 1010 Pa

• ν = 0.3

• ρ = 2700 kg/m3






• 36 grid points


Boundary Conditions

• Free conditions

• Create one constraint set (kinematic DOF) to fully constrain the three grid points shown below(grid points 7, 21, 30).

• No load case





Solution Type


Results


Normal Mode Bench Value NX Nastran ADS #Plane mode 1,2,3 0 0 1.000, 2.000, 3.000Plane mode 4,5 318.4 319.0 7.000, 8.000Plane mode 6,7 900.5 900.9 11.00, 12.00Plane mode 8,9 1727. 1724. 15.00, 16.00Plane mode 10,11 2792. 2781. 17.00, 18.00Transverse Mode1,2,3

0 0 4.000, 5.000, 6.000

Transverse Mode 4,5 511.0 511.0 9.000, 10.00Transverse Mode 6,7 1590. 1585. 13.00, 14.00Transverse Mode 8,9 3184. 3159. 19.00, 20.00

References


Thin Circular Ring Clamped at Two Points

This test is a modal analysis of a thin curved beam. It provides the input data and results forbenchmark test SDLL12/89 from Guide de validation des progiciels de calcul de structures.


Input File

sdll12.dat




Units

SI

Material Properties

• E = 7.2 x 1010 Pa

• ν = 0.3

• ρ = 2700 kg/m3



• 29 grid points





Boundary Conditions

• Points A and B: Clamped in local coordinate system

• No load case


Solution Type


Results


Normal Mode Bench Value NX Nastran1 235.3 235.92 575.3 575.23 1106. 1103.4 1406. 1399.5 1751. 1743.6 2557. 2536.7 2802. 2723.

References





Vibration Modes of a Thin Pipe Elbow

This test is a modal analysis of a straight cantilever beam, and a thin curved beam. It provides theinput data and results for benchmark test SDLL14/89 from Guide de validation des progiciels decalcul de structures.


Input Files

• sdll14a.dat (test 1, L=0)

• sdll14b.dat (test 2, L=0.6)

• sdll14c.dat (test 3, L=2.0)

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg/m3





• L = 0 or L = 0.6:

18 linear beam (CBAR) elements

19 grid points

• L = 2:

28 linear beam (CBAR) elements

29 grid points

Two of the meshes are shown in the following figure:




Boundary Conditions

• Clamp points C and D

• Point A: v = 0; w = 0

• Point B: u = 0; w = 0


Solution Type


Results


L Normal Mode Bench Value NX Nastran ADS#0 Transverse 1 44.23 44.07 1.000

Plane 1 119.0 119.2 2.000Transverse 2 125.0 125.4 3.000Plane 2 227.0 225.0 4.000

0.6000 Transverse 1 33.40 33.15 1.000Plane 1 94.00 94.42 2.000Transverse 2 100.0 98.50 3.000Plane 2 180.0 183.7 4.000

2.000 Transverse 1 17.90 17.65 1.000Plane 1 24.80 24.40 3.000Transverse 2 25.30 24.94 2.000




L Normal Mode Bench Value NX Nastran ADS#Plane 2 27.00 26.67 4.000

References


Cantilever Beam with Eccentric Lumped Mass

This test is a modal analysis of a straight cantilever beam and a lumped mass. It provides the inputdata and results for benchmark test SDLL15/89 from Guide de validation des progiciels de calcul destructures.


Input Files

• sdll15a.dat

• sdll15b.dat

Units

SI




Material Properties

• E = 2.1 x 1011 Pa

• ρ = 7800 kg/m3


Test 1:

• 10 linear beam (CBEAM) elements

• 1 rigid (RBAR) element from point B to point C

• 1 lumped mass (CONM2) element at point C

• 11 grid points

Test 2:


• 1 rigid (RBAR) element from point B to point C

• 1 lumped mass (CONM2) element at point C

• 11 grid points

The mesh both tests is is shown in the following figure:

Boundary Conditions

• Clamp point A





Solution Type

SOL 103 normal mode dynamics — SVI

Results


yc Normal Mode Bench Value NX Nastran0 Transverse 1,2 1.650 1.650

Transverse 3,4 16.07 15.88Transverse 5,6 50.02 48.64Tension 1 76.47 76.42Torsion 1 80.47 80.68Transverse 7,8 103.2 97.89

1 1 1.636 1.6332 1.642 1.6383 13.46 13.364 13.59 13.595 28.90 29.206 31.96 31.577 61.61 59.858 63.93 61.72

Mode shapes results

yc Normal Mode Modal Displacement Bench Value NX Nastran1 1 wc/wb 1.030 1.030

2 uc/vb 0.1480 –0.14803 uc/vb 2.882 –2.9044 wc/wb –0.9220 –0.9800

• wc = z displacement at point C

• wb = z displacement at point B

• uc = x displacement at point C

• vb = y displacement at point B

References





Thin Square Plate (Clamped or Free)

This test is a normal mode dynamics analysis (three-dimensional problem) of a thin plate. It providesthe input data and results for benchmark test SDLS01/89 from Guide de validation des progiciels decalcul de structures.


Input Files

• sdls01a.dat

• sdls01b.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg/m3






• 121 grid points


Boundary Conditions

• Problem 1: AB side clamped

• Problem 2: Free plate; 1 kinematic DOF set (grid points 1, 11, 111)


Solution Type





Results


Normal Mode Bench Value NX Nastran1 8.727 8.6382 21.30 20.893 53.55 52.424 68.30 65.775 77.74 75.146 136.0 127.8


Normal Mode Bench Value NX Nastran7 33.71 32.918 49.46 47.429 61.05 59.1910,11 87.52 83.08

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLS01/89..

Simply-Supported Rectangular Plate






Input Files

sdls03.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg/m3



• 176 grid points





Boundary Conditions

• Z-displacement = 0 on all sides of the plate

• One DOF set

• No load case


Solution Type


Results


Normal Mode Bench Value NX Nastran1 35.63 35.272 68.51 67.293 109.6 108.54 123.3 120.85 142.5 138.26 197.3 188.2

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLS03/89.

Thin Ring Plate Clamped on a Hub





• Re = 0.1 m

• Ri = 0.2 m

• Thickness = .001 m


Input Files

sdls04.dat

Units

SI

Material Properties

• E = 2 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg/m3






• 440 grid points


Boundary Conditions

• If r = Ri: Clamp in local coordinate system.

• No load case.





Solution Type


Results


Normal Mode Bench Value NX Nastran1 79.26 79.222,3 81.09 80.724,5 89.63 88.836,7 112.8 111.38,9 Not available 152.710,11 Not available 212.912,13 Not available 290.114,15 Not available 382.916,17 Not available 490.318 518.9 510.919,20 528.6 519.721,22 559.1 546.223 609.7 590.3

References


Vane of a Compressor - Clamped-free Thin Shell

This test is a normal mode dynamics analysis (three-dimensional problem) of a cylindrical thin shell.It provides the input data and results for benchmark test SDLS05/89 from Guide de validation desprogiciels de calcul de structures.




• α = 0.5 rad

• AD = L = 0.3048m

• r = 2L = 0.6096m

• thickness = 3.048 x 10–3 m


Input Files

• sdls05a.dat (coarse mesh)

• sdls05b.dat (fine mesh)

Units

SI

Material Properties

• E = 2.0685 x 1011 Pa

• ν = 0.3

• ρ = 7857.2 kg/m3




Finite Element Modeling — Coarse Mesh


• 121 grid points

The coarse mesh is shown in the following figure:

Finite Element Modeling — Fine Mesh


• 256 grid points

The fine mesh is shown in the following figure:




Boundary Conditions

• AD side: Clamped in local coordinate system.


Solution Type


Results


Normal Mode Bench Value NX Nastran coarsemesh

NX Nastran fine mesh

1 85.60 84.60 85.302 134.5 137.1 137.83 259.0 240.7 243.94 351.0 333.3 338.15 395.0 370.0 378.36 531.0 503.7 515.4

References


Bending of a Symmetric Truss

This test is a normal mode dynamics analysis (plane problem) of a straight cantilever beam structure.It provides the input data and results for benchmark test SDLX01/89 from Guide de validation desprogiciels de calcul de structures.




• h = 0.0048 m

• b = 0.029 m

• A = 1.392 x 10–4 m2

• Iz = 2.673 x 10–10 m4


Input File

sdlx01.dat

Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg/m3






• 24 grid points


Boundary Conditions



Solution Type





Results


Normal Mode Bench Value NX Nastran1 8.800 8.7692 29.40 29.343 43.80 43.824 56.30 56.255 96.20 95.436 102.6 102.57 147.1 146.28 174.8 173.19 178.8 177.410 206.0 202.911 266.4 262.412 320.0 309.713 335.0 321.9

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLX01/89.

Hovgaard's Problem — Pipes with Flexible Elbows

This test is a normal mode dynamics analysis (three-dimensional problem) of a straight cantileverbeam structure. It provides the input data and results for benchmark test SDLX02/89 from Guide devalidation des progiciels de calcul de structures.




• A = 0.3439 x 10E–2 m2

• R = 0.922 m

• e = 0.00612 m

• Re = 0.0925 m

• Ri = 0.08638 m

• Iy = Iz = 0.1377x10–4 m4 (straight elements)

• Iy = Iz = 0.5887x10–5 m4 (curved elements)


Input Files

sdlx02.dat

Units

SI

Material Properties

• E = 1.658 x 1011 Pa

• ν = 0.3

• ρ = 13404.106 kg/m3






• 26 grid points


Boundary Conditions






Solution Type


Results


Normal Mode Bench Value NX Nastran1 10.18 10.392 19.54 19.853 25.47 25.324 48.09 47.745 52.86 51.786 75.94 83.007 80.11 85.128 122.3 125.89 123.2 127.7

References


Rectangular Plates

This test is a normal mode dynamics analysis (three dimensional problem) of a thin plate with rigidbody modes. It provides the input data and results for benchmark test SDLX03/89 from Guide devalidation des progiciels de calcul de structures.


Input Files

sdlx03.dat




Units

SI

Material Properties

• E = 2.1 x 1011 Pa

• ν = 0.3

• ρ = 7800 kg / m3



• 320 grid points





Boundary Conditions

• Free plate

• One DOF set


Solution Type


Results


Normal Mode Bench Value NX Nastran1 584.0 577.02 826.0 813.03 855.0 844.04 911.0 895.05 1113. 1062.6 1136. 1118.

References





Mechanical Structures — Normal Mode Dynamics Analysis andModel Response

Transient Response of a Spring-Mass System with Acceleration Loading

This test is an undamped transient response by modal superposition. It provides the input data andresults for benchmark test SDLD04/89 from Guide de validation des progiciels de calcul de structures.

Where:

• m = 1 kg

• k = 1000 N/m


Input Files

sdld04.dat

Units

SI

Material Properties

Spring constant.


• 3 lumped mass (CONM) elements

• 3 translational spring (CELAS) elements





Boundary Conditions

• Points A: Clamped (u = v = 0 : θ - 0)

• Points B, C and D: v = 0 ; = 0

• Point A: Set acceleration: ű(t) = 2E5 * (t2) ; (0 < t < 0.1 s)

• Initial condition: u(0) = 0 ; u(0) = 0 at every point

The mesh and the boundary conditions are shown in the following figure:

Solution Type

SOL 112 — Modal Transient Response

Results

The mode shapes results are exact.


Normal Mode Bench Value NX Nastran1 2.239 2.2392 6.275 6.2753 9.069 9.069

Mode shapes results

Normal Mode Point Bench Value NX Nastran1 B 0.4450 0.4450

C 0.8019 0.8019D 1.000 1.000

2 B 1.000 1.000C 0.4450 0.4450D –0.8019 –0.8019B –0.8019 –0.8019C 1.000 1.000D –0.4450 –0.4450




Transient response (Point D: X-displacement in meters)

Time (sec) Bench Value NX Nastran0.02000 –0.002700 –0.0026700.04000 –0.04260 –0.042700.05000 –0.1041 –0.10410.06000 –0.2158 –0.21600.08000 –0.6813 –0.68180.1000 –1.658 –1.659

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. SDLD04/89.




Transient Response of a Clamped-free Post

This test is a transient response of a straight cantilever beam with acceleration and force loadings,and modal damping. It provides the input data and results for benchmark test SDLL06/89 from "Guidede validation des progiciels de calcul de structures."


Input Files

sdll06.dat

Units

SI

Material Properties

• E = 4 x 1010 Pa

• Iz = 3.285 x 10–1 m4

• ρ = 0



• 9 grid points





Boundary Conditions

To apply an acceleration üA(t) at point A, we can do the following:

• Points A: Clamped (u = v = 0 : θ - 0)

• Point B: Set nodal force Fx(t) equal to mB * üA(t) in the -X direction

Fx(t) = –m * üA(t)

• Initial conditions: u(0) = 0 ; u (0) = 0 at every point

The mesh and the boundary conditions are shown in the following figure:




Solution Type

SOL 109 — Direct Transient Response

Results

uB displacement (mm)

Time (s) Bench Value NX Nastran0.01000 –0.06500 –0.065700.02000 –0.5130 –0.51520.03000 –1.679 –1.6820.04000 –3.457 –3.4640.05000 –5.316 –5.3330.06000 –6.764 –6.8040.07000 –7.609 –7.6820.08000 –7.774 –7.8910.09000 –7.244 –7.4130.1000 –6.068 –6.2890.1200 –2.242 –2.5420.1400 2.367 2.0700.1600 6.149 5.9770.1800 7.783 7.8470.2000 6.698 7.042

The problem with damping is not computed.




References


Stationary Thermal Tests — Heat Transfer Analysis

Hollow Cylinder - Fixed Temperatures

This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with fixedtemperatures. It provides the input data and results for benchmark test TPLA01/89 from "Guide devalidation des progiciels de calcul de structures."




• Re = 0.30 m

• Ri = 0.35 m


Input Files

htpla01.dat

Units

SI

Material Properties

• λ = 1 W/m °C


• 5 linear axisymmetric solid CQUADX4 elements and 5 parabolic axisymmetric solid CQUADX8elements

• 10 linear axisymmetric solid CTRAX3 elements and 10 parabolic axisymmetric solid CTRAX6elements

The triangular element mesh is shown in the following figure:




Boundary Conditions

• One temperature set:

– Internal temperature Ti = 100 °C

– External temperature Te = 20 °C

Solution Type

SOL 153 — Steady State Heat Transfer

Results

Temperature results

Radius (m) Bench Value(°C)

NX Nastran(°C)

CTRAX3

NX Nastran(°C)

CTRAX6

NX Nastran(°C)

CQUADX4

NX Nastran(°C)

CQUADX80.3000 100.0 100.0 100.0 100.0 100.00.3100 82.98 82.98 82.98 82.98 82.980.3200 66.51 66.51 66.51 66.51 66.510.3300 50.54 50.54 50.54 50.54 50.540.3400 35.04 35.04 35.04 35.04 35.040.3500 20.00 20.00 20.00 20.00 20.00

Flux results

Radius (m) Bench Value(W/m2)

NX Nastran(W/m2)CTRAX3

NX Nastran(W/m2)CTRAX6

NX Nastran(W/m2)

CQUADX4

NX Nastran(W/m2)

CQUADX80.3000 1730. 1702. 1711. 1702. 1702.0.3100 1674. 1675. 1674. 1675. 1675.0.3200 1622. 1622. 1622. 1622. 1622.0.3300 1573. 1573. 1573. 1573. 1573.0.3400 1526. 1527. 1527. 1527. 1527.0.3500 1483. 1505. 1497. 1504. 1504.

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. TPLA01/89.




Hollow Cylinder - Convection

This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with convection. Itprovides the input data and results for benchmark test TPLA03/89 from "Guide de validation desprogiciels de calcul de structures."

• Re = 0.300 m

• Ri = 0.391 m


Input Files

htpla03.dat

Units

SI

Material Properties

• λ = 40.0 W/m °C


• 11 linear axisymmetric solid CQUADX4 elements and 1 parabolic axisymmetric solid CQUADX8element

• 22 linear axisymmetric solid CTRAX3 elements and 2 parabolic axisymmetric solid CTRAX6elements





Boundary Conditions

• Convection on internal surface:

hi = 150.0 W/m2 / °C

Ti = 500 °C

• Convection on external surface:

he = 142.0 W/m2 / °C

Ti = 20 °C

Solution Type


Results

Temperature/ Flux Bench Value NX Nastran

CTRAX3NX NastranCTRAX6

NX NastranCQUADX4

NX NastranCQUADX8

Ti (°C) 272.3 272.2 272.4 272.5 272.4Te (°C) 205.1 204.6 204.5 204.6 204.5φi (W/m2) 3.416E4 3.20E4 3.11E4 1.56E4 2.98E4φe (W/m2) 2.628E4 2.77E4 2.85E4 1.56E4 2.98E4

φ / l = φ * 2 * π * R

So: φ / l= 34173.82 * 2 * π * 0.300 = 64416.13 W/m

References





Cylindrical Rod - Flux Density

This test is a steady-state heat transfer analysis of a 2D axisymmetric rod with fixed temperaturesand flux density. It provides the input data and results for benchmark test TPLA05/89 from "Guide devalidation des progiciels de calcul de structures."


Input Files

htpla05.dat

Units

SI

Material Properties

• λ = 33.33 W/m °C


• 40 linear axisymmetric solid CTRAX3 elements

• 20 linear axisymmetric solid CQUADX4 elements




The quadrilateral element mesh is shown in the following figure:

Boundary Conditions

• z = 0

Set temperature to 0 °C

• z = 1


• Cylindrical surface

Set flux to –200 W/m2





Solution Type

SOL 153 — Steady State Heat transfer

Temperature results (°C)

Grid Point # z (m) Bench value NX Nastran(CTRAX3)

NX Nastran(CQUADX4)

Grid point 3 0.0000 0.000 0.000 0.000Grid point 41 0.1000 -4.000 -4.020 -4.020Grid point 39 0.2000 4.000 3.980 3.980Grid point 37 0.3000 24.00 23.97 23.97Grid point 35 0.4000 56.00 55.97 55.97Grid point 33 0.5000 100.0 99.97 99.97Grid point 31 0.6000 156.0 156.0 156.0Grid point 29 0.7000 224.0 224.0 224.0Grid point 27 0.8000 304.0 304.0 304.0Grid point 25 0.9000 396.0 396.0 396.0Grid point 4 1.000 500.0 500.0 500.0

Results are post-processed on the internal surface. NX Nastran does not make the approximation, T= cte when r is fixed.

References


Hollow Cylinder with Two Materials - Convection

This test is a steady-state heat transfer analysis of a 2D axisymmetric cylinder with two materialsand convection. It provides the input data and results for benchmark test TPLA08/89 from "Guide devalidation des progiciels de calcul de structures."




• Ri = 0.30 m

• Rm = 0.35 m

• Re = 0.37 m


Input Files

htpla08.dat

Units

SI

Material Properties

• Material 1: λ1 = 40.0 W/m °C



• 14 linear axisymmetric solid CTRAX3 elements

• 7 linear axisymmetric solid CQUADX4 elements





Boundary Conditions

• Convection on internal surface

hi = 150.0 W/m2 °C

Ti = 70 °C

• Convection on external surface

he = 200.0 W/m2 °C

Te = –15 °C

Solution Type


Results

Grid point # TemperatureFlux

Bench Value NX Nastran(CTRAX3)

NX Nastran(CQUADX4)

Grid point 9 Ti (°C) 25.42 25.45 25.45Grid point 14 Tm (°C) 17.69 17.68 17.68Grid point 16 Te (°C) 12.11 12.09 12.11Grid point 9 φi (W/m2) 6687. 6609. 6558.Grid point 14 φm (W/m2) 5732. 5768. 5733.Grid point 16 φe (W/m2) 5422. 5497. 5497.

φ/l = φ * 2 * π * R

So: φ/l= 5733.33 * 2 * π * 0.35 = 12608.25 W/m




References


Wall-Convection

This test is a steady-state heat transfer analysis of a 1D wall with fixed convection. It provides theinput data and results for benchmark test TPLL03/89 from "Guide de validation des progiciels decalcul de structures."


Input Files

htpl03.dat

Units

SI

Material Properties

• λ = 1.0 W/m °C


• 1 linear quadrilateral thin shell (CQUAD4) element

• 4 grid points

The thin shell element thickness is set to 1 m.





Boundary Conditions


hA = 20.0 W/m2 °C

TA = –20.0 °C

• Convection on external surface

hB = 10.0 W/m2 °C

TB = 500.0 °C

• Convection coefficient is defined as

energy / (length * time * temperature) in the current system of units.


Solution Type





Results


Grid point # Temperature/Flux Bench Value NX NastranGrid point 2 TA (°C) 21.71 21.71Grid point 4 TB (°C) 416.6 416.6Grid point 1 (W/m2) 834.2 834.3

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. TPLL03/89.

Wall-Fixed Temperatures

This test is a steady-state heat transfer analysis of a 1D wall with fixed temperatures. It provides theinput data and results for benchmark test TPLL01/89 from "Guide de validation des progiciels decalcul de structures."






Input Files

htpl01.dat

Units

SI

Material Properties

• λ = 0.75 W/m °C



• 6 grid points

Boundary Conditions

• Internal temperature Ti = 100 °C

• External temperature Te = 20 °C

Solution Type


Results


Grid point # Length: x (m) Bench Value NX NastranGrid point 1 0 100.0 100.0Grid point 3 0.01000 84.00 84.00Grid point 4 0.02000 68.00 68.00Grid point 5 0.03000 52.00 52.00Grid point 6 0.04000 36.00 36.00Grid point 2 0.05000 20.00 20.00

The flux calculated with NX Nastran is exact:

= 1200 Ω / μ2

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No. TPLL01/89.




L-Plate

This test is a steady-state heat transfer analysis of a 2D L-plate with fixed temperatures. It providesthe input data and results for benchmark test TPLP01/89 from "Guide de validation des progiciels decalcul de structures."


Input Files

htpp01a.dat - linear quadrilateral thin shell elements

htpp01b.dat - parabolic quadrilateral thin shell elements

Units

SI

Material Properties

• λ = 1.0 W/m °C


• Test 1 – 12 linear quadrilateral thin shell (CQUAD4) elements

• Test 2 – 12 parabolic quadrilateral thin shell (CQUAD8) elements





Boundary Conditions

• AF side


• DE side


Solution Type

SOL153 — Steady State Heat Transfer

Results

Temperature Results (°C)

Node Bench Value NX Nastran CQUAD4 NX Nastran CQUAD88 7.869 7.924 7.8829 5.495 5.613 5.519




Node Bench Value NX Nastran CQUAD4 NX Nastran CQUAD810 2.816 2.885 2.83419 8.018 8.043 8.01518 5.680 5.821 5.66520 2.881 2.963 2.87717 8.514 8.425 8.5186 6.667 6.667 6.66716 2.972 3.148 2.96221 9.001 8.992 9.10715 8.640 8.356 8.66814 9.316 9.189 9.2825 9.009 8.773 8.961

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No.TPLP01/89.

Orthotropic Square

This test is a steady-state heat transfer analysis of a square plate with orthotropic conduction andconvection. It provides the input data and results for benchmark test TPLP02/89 from "Guide devalidation des progiciels de calcul de structures."


Input Files

htpp02.dat

Units

SI




Material Properties

• λx = 1.00 W/m °C

• λx =.75 W/m °C



• 121 grid points

The thin shell element thickness is set to 1 m.


Boundary Conditions

• Flux density y = 60 W/m2 for face y = –0.1. (Entry)

• Flux density y = –60 W/m2 for face y = 0.1. (Exit)

• Convection on the faces X = –0.1 and x = 0.1:

– h = 15.0 W/m2 °C

• Linear variation of the external temperatures:

– Te = 30 – 80y on the face x = –0.1

– Te = 15 – 80y on the face x = 0.1

• Convection coefficient is defined as:

– Energy / (length * time * temperature)

• Flux density is defined as:

– Energy / (length * time) in the current system of units





Solution Type


Results

Temperature Results

Point Bench Value (°C) NX Nastran (°C)0 22.50 22.50A 35.00 34.80B 26.00 25.80C 10.00 10.20D 19.00 19.20

E 30.50 30.50F 18.00 18.00G 14.50 14.50H 27.00 27.00

Flux Results (W/m2)

Grid Point Bench Value NX Nastran

61 X 45.00 45.0061 Y 60.00 59.55




References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No.TPLP02/89.

Hollow Sphere - Fixed Temperatures, Convection

This test is a steady-state heat transfer analysis of a 3D sphere with fixed temperatures andconvection. It provides the input data and results for benchmark test TPLV02/89 from "Guide devalidation des progiciels de calcul de structures."

• Ri = 0.30 m

• Re = 0.35 m


Input Files

htpv02.dat (CHEXA and CPENTA)

htpv02p.dat (CPYRAM and CPENTA)

Units

SI

Material Properties

• λ = 1 W/m °C


Test 1: Brick and wedge element test

• 500 linear brick (CHEXA) and linear wedge (CPENTA) elements

• 766 grid points

The test is executed on 1/8 mapped meshed sphere.





Test 2: Pyramid and wedge element test

• Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into 6pyramid elements. Linear wedge (CPENTA) elements remain.

Boundary Conditions


hi = 30 W/m2 °C

Ti = 100 °C

• Set external surface temperature Te to 20 °C

The load sets are shown in the following figure:




Solution Type


Results


Test Radius r (m) Bench Value NX NastranTest 1 0.3000 65.00 64.88Test 2 0.3000 65.00 64.86Test 1 0.3100 54.84 54.75Test 2 0.3100 54.84 54.72Test 1 0.3200 45.31 45.25Test 2 0.3200 45.31 45.23Test 1 0.3300 36.36 36.33Test 2 0.3300 36.36 36.30Test 1 0.3400 27.94 27.92Test 2 0.3400 27.94 27.91Test 1 0.3500 20.00 20.00Test 2 0.3500 20.00 20.00

Flux results (W/m 2): (X-direction)

Test Radius r (m) Bench Value NX NastranTest 1 0.3000 1050. 1013.Test 2 0.3000 1050. 1013.Test 1 0.3100 983.4 981.4Test 2 0.3100 983.4 981.6Test 1 0.3200 922.9 921.2Test 2 0.3200 922.9 921.3Test 1 0.3300 867.5 866.3




Test Radius r (m) Bench Value NX NastranTest 2 0.3300 867.5 866.3Test 1 0.3400 817.5 816.3Test 2 0.3400 817.5 816.1Test 1 0.3500 771.4 792.4Test 2 0.3500 771.4 792.1

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No.TPLV02/89.

Hollow Sphere with Two Materials - Convection

This test is a steady-state heat transfer analysis of a 3D sphere with two materials and convection.It provides the input data and results for benchmark test TPLV04/89 from "Guide de validation desprogiciels de calcul de structures."

• Ri = 0.30 m

• Rm = 0.35 m

• Re = 0.37 m


Input Files

htpv04a.dat (CHEXA and CPENTA elements)

htpv04b.dat (CTETRA elements)

htpv04c.dat (CTRAX6 elements)

htpv04p.dat (CPYRAM and CPENTA elements)




Units

SI

Material Properties




• Test 1 - 700 linear brick (CHEXA) and linear wedge (CPENTA) elements

• Test 2 - 2192 parabolic tetrahedron (CTETRA) elements

• Test 3 - 8 parabolic axisymmetric (CTRAX6) elements

• Test 4- Linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into6 pyramid elements. Linear wedge (CPENTA) elements remain.

The test is executed on a 1/8 meshed sphere





Boundary Conditions

• Convection on internal surface:

hi = 150.0 W/m2 °C

Ti = 70 °C

• Convection on external surface:

he = 200.0 W/m2 °C

Te = –9 °C





Solution Type


Results

Temperature Results

Temperature/ Flux

BenchValue

CHEXA &CPENTA

CTETRA CTRAX6 CPYRAM &CPENTA

Ti (°C) 25.06 N1 25.02 N19 25.06 24.98 N1 23.66Tm (°C) 17.84 N556 17.84 N9 17.84 17.72 N556 16.26Te (°C) 13.16 N778 13.18 N5 13.15 13.17 N778 13.85φi (W/m2) 6741. N1 6487. N19 5865. 6390. N1 6683.φm (W/m2) 4952. N556 4931. N9 4765. 4819. N556 5080.φe (W/m2) 4431. N778 4531. N5 4551. 4508. N778 4669.

φ = φ * 4 * π * R2

So: φ = 4931.20 * 4 * π * 0.352 = 7590.00 W

Flux is in the x direction

References





Thermo-mechanical Tests — Linear Statics Analysis

Orthotropic Cube

This test is a steady-state heat transfer analysis of a 3D cube with convection and flux density. Itprovides the input data and results for benchmark test TPLV07/89 from "Guide de validation desprogiciels de calcul de structures."


Input Files

htpv07.dat (CHEXA)

htpv07p.dat (CPYRAM)

Units

SI

Material Properties

• λx = 1.00 W/m °C

• λy = 0.75 W/m °C

• λz = 0.50 W/m °C


Test 1: Brick element test


• 729 grid points





Test 2: Pyramid element test

• 3072 linear pyramid (CPYRAM) elements created by dividing each brick element in test 1 into6 pyramid elements.

Boundary Conditions

• Flux density y = 60 W/m2 for face y = –0.1 (Entry)

• Flux density y = –60 W/m2 for face y = 0.1 (Exit)

• Flux density z = 30 W/m2 for face z = –0.1 (Entry)

• Flux density z = –30 W/m2 for face z = 0.1 (Exit)

• Convection on the faces X = –0.1 and x = 0.1:

–h = 15.0 W/m2 °C

• Linear variation of the external temperatures:

–Te = 30 – 80y – 60z on the face x = –0.1

–Te = 15 – 80y – 60z on the face x = 0.1





Solution Type


Results


Test Point Bench Value NX NastranTest1 A 35.00 34.70Test2 A 35.00 34.70Test1 B 26.00 25.70Test2 B 26.00 25.70Test1 C 10.00 10.30Test2 C 10.00 10.30Test1 D 19.00 19.30Test2 D 19.00 19.30Test1 S 30.50 30.40Test2 S 30.50 30.40Test1 F 18.00 18.00Test2 F 18.00 18.00Test1 M 14.50 14.60Test2 M 14.50 17.70Test1 H 27.00 27.00Test2 H 27.00 27.00




Test Point Bench Value NX NastranTest1 N 29.00 29.00Test2 N 29.00 29.00Test1 P 20.00 20.00Test2 P 20.00 20.00Test1 J 4.000 4.600Test2 J 4.000 4.590Test1 I 13.00 13.60Test2 I 13.00 13.60Test1 E 16.50 16.60Test2 E 16.50 16.60Test1 R 41.00 40.40Test2 R 41.00 40.40Test1 Q 32.00 31.40Test2 Q 32.00 31.40Test1 K 16.00 16.00Test2 K 16.00 16.00Test1 L 25.00 25.00Test2 L 25.00 25.00Test1 G 28.50 28.40Test2 G 28.50 28.40

References


Thermal Gradient on a Thin Pipe

This test is a thermo-mechanical linear statics analysis of a thin pipe with thermal gradient andplane strain. It provides the input data and results for benchmark test HSLA01/89 from "Guide devalidation des progiciels de calcul de structures."




• Ri = 0.020 m

• Re = 0.025 m


Input Files

hsla01.dat

Units

SI

Material Properties

• E = 1.0 x 1011 Pa

• ν = 0.3

• Coefficient of expansion: α = 1.0 x 10–5/°C


• 1000 linear axisymmetric solid (CTRAX3) elements

• 500 linear axisymmetric solid (CQUADX4) elements




The quadrilateral element mesh is shown in the following figure:

Boundary Conditions

• Articulate AB side

• Radial temperature with Ti = 100 °C, and Te = 0 °C.





Solution Type

SOL 101 Linear statics

Results

Point Stress Bench Value(Pa)

NX Nastran(Pa)(CTRAX3)

NX Nastran(Pa)(CQUADX4)

r = Ri σr 0 –14.03E6 –0.848E6σθ –74.07E6 –79.84E6 –74.26E6

r = (Re + Ri) / 2 σr –3.950E6 –3.908E6 –3.890E6σθ 1.306E6 1.469E6 1.390E6

r = Re σr 0 –11.31E6 –0.649E6σθ 68.78E6 73.69E6 68.48E6

References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No.HSLA01/89.

Simply-Supported Arch

This test is a thermo-mechanical linear statics analysis of a thin curved beam with thermal gradientand articulation. It provides the input data and results for benchmark test HSLL01/89 from "Guide devalidation des progiciels de calcul de structures."

• R = 10 m

• A = 144 x 10–4 m2

• I = 1.728 x 10–5 m4

Beam cross section:





Input Files

hsll01.dat

Units

SI

Material Properties

• E = 0.2 x 1011 Pa

• = 0.3

• Coefficient of expansion: α = 11.0 x 10–6/C°



• 51 grid points


Boundary Conditions

• Articulate point A and B




• Top temperature Ts = 160 °C

• Middle temperature Tm = 100 °C

• Bottom temperature Ti = 40 °C


Solution Type


Results

Point Force Moment Bench Value NX Nastranθ = π/2 M 0 4.040 e–5

N 0 15.10T –479.2 –527.6

θ = π/4 M 3388. 3729.N –338.8 –373.2T –338.8 –373.2

θ = 0 M 4792. 5277.N –479.2 527.5T 0 15.00

Post Processing

List the beam forces

• M - Z bending moment

• N - axial force

• T - Y shear force




References

Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures. Paris,Afnor Technique, 1990. Test No.HSLL01/89.



Chapter 7: Material Nonlinear (Plasticity) VerificationUsing Standard NAFEMS Benchmarks

7.1 Overview of the Material Nonlinear (Plasticity) Verification UsingNAFEMS Test CasesThe purpose of this section is to verify the accuracy and robustness of NX Nastran. The plasticityverification uses test cases published by the National Agency for Finite Element Methods andStandards (NAFEMS) in Fundamental Tests for Two and Three Dimensional, Small Strain,Elastoplastic Finite Element Analysis. (See Reference.)

To perform the tests, input data is applied to single elements including plane strain elements,plane stress elements, axisymmetric solid elements, and solid elements. Results are tabulatedand compared to results published by NAFEMS.

The plasticity verification includes perfect plasticity and isotropic hardening tests. Within thesecategories, results for uniaxial, biaxial, and triaxial displacement tests are provided.

Understanding the Verification Format

The format for the nonlinear section of the Solver Verification document looks somewhat differentfrom the linear section. Each test case in this section provides a brief description of the test includinginput data. The results are then displayed in the form of a graph comparing NX Nastran Nonlinearresults published by NAFEMS for the same test case.

Reference

The following reference has been used in the NX Nastran Plasticity verification problems:

Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain,Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite ElementMethods and Standards, April, 1987.


Chapter 7: Material Nonlinear (Plasticity) Verification Using Standard NAFEMS Benchmarks

Test Cases

Plane Strain Elements - Perfect Plasticity Tests

This article provides input data and results for perfect plasticity tests including prescribed uniaxial andprescribed biaxial displacement tests. The tests were run on these plane stress elements:

• Linear triangle (CTRIA3) elements

• Linear quadrilateral (CQUAD4) elements

The material description and initial boundary conditions are the same for the uniaxial and biaxialdisplacement tests.


Input Files

nlspls89.dat (uniaxial)

nlspls90.dat (biaxial)

Units

Inch

Attributes

Load Control

Material Properties

• E = 250000.0

• = 0.25

• σy = 5.0

• H = 0.0

• εo = 0.000025 (strain at first yield)



Material Nonlinear (Plasticity) Verification Using Standard NAFEMS Benchmarks

Boundary Conditions

The following figure shows the plane strain elements and the boundary conditions applied toeach. The strain state is completely defined as a function of time since all degrees of freedom aresuppressed or prescribed.

These boundary conditions represent initial conditions only and do not illustrate the time history ofthe applied conditions.




Results

Uniaxial Displacement Test — Applied Strain History

The following graph shows results of the uniaxial displacement test for the plane strain elements.

Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults compared with NAFEMS test results for plane strain with perfect plasticity.

History Strain XX Strain YY Strain ZZ1 0.2500D–4 0D+00 0D+002 0.5000D–4 0D+00 0D+003 0.2500D–4 0D+00 0D+004 0D+00 0D+00 0D+00

10 increments per strain history step




Biaxial Displacement Test — Applied Strain History

The following graph shows results of the biaxial displacement test for the plane strain elements.

Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults (points) compared to NAFEMS test results for plane strain with perfect plasticity.

History Stage Strain XX Strain YY Strain ZZ1 0.2500D–4 0D+00 0D–002 0.5000D–4 0D+00 0D–003 0.5000D–4 0.2500D–4 0D–004 0.5000D–4 0.5000D–4 0D–005 0.2500D–4 0.5000D–4 0D–006 0D+00 0.5000D–4 0D+007 0D+00 0.2500D–4 0D+008 0D+00 0D+00 0D+00





References

Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain,Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite ElementMethods and Standards, April, 1987 pp. 2.3-2.25.

Plane Strain Elements - Isotropic Hardening Tests

This article provides input data and results for isotropic hardening tests including prescribed uniaxialand prescribed biaxial displacement tests. The tests were run on these plane strain elements:





Input Files

nlspls91.dat (uniaxial)

nlspls92.dat (biaxial)

Units

Inch

Attributes

Load Control

Material Properties

• E = 250000.0

• = 0.25

• σy = 5.0

• H = 62500.0




• εo = 0.000025 (strain at first yield)

Boundary Conditions






Results



Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults (points) compared to NAFEMS test results for plane strain with isotropic hardening.

History Strain XX Strain YY Strain ZZ1 0.2500D–4 0D+00 0D+002 0.5000D–4 0D+00 0D+003 0.2500D–4 0D+00 0D+004 0D–00 0D+00 0D+00







Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults (points) compared to NAFEMS test result for plane strain with isotropic hardening.

History Stage Strain XX Strain YY Strain ZZ1 0.2500D–4 0D+00 0D+002 0.5000D–4 0D+00 0D+003 0.5000D–4 0.2500D–4 0D+004 0.5000D–4 0.5000D–4 0D+005 0.2500D–4 0.5000D–4 0D+006 0D–00 0.5000D–4 0D+007 0D–00 0.2500D–4 0D+008 0D–00 0D–00 0D+00





References

Hinton, E., and Ezatt, M.H. Fundamental Tests for Two and Three Dimensional, Small Strain,Elastoplastic Finite Element Analysis. East Kilbride, Glasgow, UK: National Agency for Finite ElementMethods and Standards, April, 1987 pp. 2.26 - 2.35.

Plane Stress Elements - Perfect Plasticity Tests

This article provides input data and results for perfect plasticity tests including prescribed uniaxial andprescribed biaxial displacement tests. The tests were run on these plane strain elements:




The following figure shows the geometry:


Input Files

nlspls61.dat (uniaxial test), linear quadrilateral (CQUAD4) elements

nlspls62.dat (uniaxial test), linear triangle (CTRIA3) elements

nlspls65.dat (biaxial test), linear quadrilateral (CQUAD4) elements

nlspls66.dat (biaxial test), linear triangle (CTRIA3) elements

Units

Inch

Material Properties

• E = 250000.0

• = 0.25

• σy = 5.0




• H = 0.0

• o = 0.2080126 x 10–4 (strain at first yield)

Boundary Conditions






Results



Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults (points) compared to NAFEMS test results for plane stress with perfect plasticity.

History Strain XX Strain YY Strain ZZ1 0.2080D–4 0D+00 -0.6934D–52 0.4160D–4 0D+00 -0.2538D–43 0.2080D–4 0D+00 -0.1835D–44 0.4235D–21 0D+00 -0.1128D–4







Results are exactly the same for both elements. The graph shows the NX Nastran Nonlinear testresults (points) compared to NAFEMS test results.

History Stage Strain XX Strain YY Strain ZZ1 0.2080D–4 0D+00 -0.6934D–52 0.4160D–4 0D+00 -0.2528D–43 0.4160D–4 0.2080D–4 -0.4284D–44 0.4160D–4 0.4160D–4 -0.6513D–45 0D–00 0.4160D–4 -0.5035D–46 0D–00 0.1872D–4 -0.3871D–47 0D–00 0D–00 -0.1867D–4


References





Plane Stress Elements - Isotropic Hardening Tests

This article provides input data and results for isotropic hardening tests including prescribed uniaxialand prescribed biaxial displacement tests. The tests were run on the these plane stress elements:




The following figure shows the geometry:


Input Files

nlspls71.dat (uniaxial test), linear quadrilateral (CQUAD4) elements

nlspls72.dat (uniaxial test), linear triangle (CTRIA3) elements

nlspls75.dat (biaxial test), linear quadrilateral (CQUAD4) elements

nlspls76.dat (biaxial test), linear triangle (CTRIA3) elements

Units

Inch

Material Properties

• E = 250000.0

• = 0.25

• σy = 5.0

• H = 62500.0

• o = 0.2080126 x 10–4 (strain at first yield)




Boundary Conditions


These boundary conditions represent initial conditions only and do not show the time history ofthe applied conditions.




Results




History Strain XX Strain YY Strain ZZ1 0.2080D–4 0D+00 -0.6934D–52 0.4160D–4 0D+00 -0.2249D–43 0.2080D–4 0D+00 -0.1555D–44 0.4235D–21 0D+00 -0.8619D–5








History Stage Strain XX Strain YY Strain ZZ1 0.2080D–4 0D+00 -0.6934D–52 0.4160D–4 0D+00 -0.2249D–43 0.4160D–4 0.2080D–4 -0.3569D–44 0.4160D–4 0.4160D–4 -0.5406D–45 0.2080D–4 0.4160D–4 -0.4712D–46 0D–00 0.4160D–4 -0.4102D–47 0D–00 0.2080D–4 -0.3408D–48 0D–00 0D–00 -0.2715D–4





References


Solid Element - Perfect Plasticity Tests

This article provides input data and results for perfect plasticity tests including prescribed uniaxial,biaxial, and triaxial displacement tests. The tests were run on the solid parabolic brick element.


Input Files

nlspls08.dat

Units

Inch

Material Properties

• E = 250000.0

• = 0.25

• y = 5.0

• H = 0.0

• o = 0.000025 (strain at first yield)

Boundary Conditions

The following figure shows the parabolic brick (CHEXA) element and the boundary conditions appliedto it. The strain state is completely defined as a function of time since all degrees of freedom aresuppressed or prescribed.





Results


History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 2.500E–5 0E+00 0E+004 0E+00 0E+00 0E+00





The following graph shows results of the uniaxial displacement test for the solid brick element. Itshows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.





The following graph shows results of the biaxial displacement test for the solid brick element. Thegraph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.

History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 5.000E–5 2.500E–5 0E+004 5.000E–5 5.000E–5 0E+005 2.500E–5 5.000E–5 0E+006 0E+00 5.000E–5 0E+007 0E+00 2.500E–5 0E+008 0E+00 0E+00 0E+00

- 10 increments per strain history step




Triaxial Displacement Test — Applied Strain History

The following graph shows results of the triaxial displacement test for the solid brick element. Thegraph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.

History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 5.000E–5 2.500E–5 0E+004 5.000E–5 5.000E–5 0E+005 5.000E–5 5.000E–5 2.500E–56 5.000E–5 5.000E–5 5.000E–57 2.500E–5 5.000E–5 5.000E–58 0E+00 5.000E–5 5.000E–59 0E+00 2.500E–5 5.000E–510 0E+00 0E+00 5.000E–511 0E+00 0E+00 2.500E– 512 0E+00 0E+00 0E+00





References


Solid Element - Isotropic Hardening Tests

This article provides input data and results for isotropic hardening tests including prescribed uniaxial,biaxial, and triaxial displacement tests. The tests were run on the solid parabolic brick element(CHEXA), which has 20 grid points.


Input Files

nlspls09.dat

Units

Inch

Material Properties

• E = 250000.0

• = 0.25

• y = 5.0

• H = 62500.0

• o = 0.000025 (strain at first yield)

Boundary Conditions

The following figure shows the parabolic brick element and the boundary conditions applied toit. The strain state is completely defined as a function of time since all degrees of freedom aresuppressed or prescribed.





Results


The following graph shows results of the uniaxial displacement test for the solid brick element. Itshows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.

History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 2.500E–5 0E+00 0E+004 0E+00 0E+00 0E+00






The following graph shows results of the biaxial displacement test for the solid brick element. Thegraph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.

History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 5.000E–5 2.500E–5 0E+004 5.000E–5 5.000E–5 0E+005 2.500E–5 5.000E–5 0E+006 0E+00 5.000E–5 0E+007 0E+00 2.500E–5 0E+008 0E+00 0E+00 0E+00





Triaxial Displacement Test — Applied Strain History

The following graph shows results of the triaxial displacement test for the solid brick element. Thegraph shows the NX Nastran Nonlinear test results (points) compared to NAFEMS test results.

History Strain XX Strain YY Strain ZZ1 2.500E–5 0E+00 0E+002 5.000E–5 0E+00 0E+003 5.000E–5 2.500E–5 0E+004 5.000E–5 5.000E–5 0E+005 5.000E–5 5.000E–5 2.500E–56 5.000E–5 5.000E–5 5.000E–57 2.500E–5 5.000E–5 5.000E–58 0E+00 5.000E–5 5.000E–59 0E+00 2.500E–5 5.000E–510 0E+00 0E+00 5.000E–511 0E+00 0E+00 2.500E–512 0E+00 0E+00 0E+00





References




Chapter 8: Geometric Nonlinear Verification UsingStandard NAFEMS Benchmarks

8.1 Overview of the Geometric Nonlinear Verification UsingNAFEMS Test CasesThis section verifies the accuracy and robustness of the arc-length method of NX Nastran. Thegeometric nonlinear verification uses test cases published by the National Agency for Finite ElementMethods and Standards (NAFEMS) in NAFEMS Non-Linear Benchmarks and A Review of BenchmarkProblems for Geometric Non-linear Behaviour of 3-D Beams and Shells. (See References.)

Understanding the Verification Format

Each test case includes the following information.


- Units

- Material properties

- Finite element modeling information

- Boundary conditions (loads and restraints)

- Solution type

• Results — time history versus Load Factor plots are presented. (Note that in NX Nastran, theload factor is displayed as "eigenvalue".)

• Reference

Reference

The following references have been used for these verification problems:

• NAFEMS Non-Linear Benchmarks. Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.

• NAFEMS, A Review of Benchmark Problems for Geometric Non-Linear Behaviour of 3-D Beamsand Shells (Summary) (Glasgow: NAFEMS, Ref. R0024.)


Chapter 8: Geometric Nonlinear Verification Using Standard NAFEMS Benchmarks

Test Cases

Straight Cantilever with End Moment

This test is a nonlinear analysis of a single row of equal-sized elements. This document provides theinput data and results for NAFEMS Non-linear Benchmarks NL5.

Test attributes:

• Bending action only

• Initially straight elements

• Load control


Input Files

nfnl05a.dat (load control)

nfnl05b.dat (arc-length control)

Units

SI

Material Properties

• E = 210 x 109 N / m2

• = 0.0

SI


32 linear beam (CBEAM) elements



Geometric Nonlinear Verification Using Standard NAFEMS Benchmarks

Boundary Conditions

• U = V = = 0 at point B

• Concentrated load at Point A applied in equal increments up to a maximum value of M L / 2 πE I = 1.0

Solution Type

SOL 106 — Geometric Nonlinear

• Loading method — arc-length control.

• Adaptive search control:

– Initial increment factor = 0.05

– Target number of iterations = 6

– Maximum number of splits = 3

– Max increment factor = 1

– Number of reporting steps = 18

Geometric nonlinear 2




• Loading method — load control.

• 6 equal steps.

Results

Normalizing Constants

• 2 E I / L = 3436.12 x 103 Nm

• L = 3.2 m

• 2 = 6.28319

Graphs of Results

• Free end axial displacement vs. Load Factor




• Vertical displacement at grid point 33 vs. Load Factor




• Rotational displacement at grid point 33 vs. Load Factor

References

National Agency for Finite Element Methods and Standards, NAFEMS Non-Linear Benchmarks(Glasgow: NAFEMS, Oct., 1989., Rev. 1). Test No. NL5.

Straight Cantilever with Axial End Point Load - Brick Elements

This test is a nonlinear analysis of a straight cantilever with an axial end point load, made up of asingle row of straight elements. This document provides the input data and results for NAFEMSNon-linear Benchmarks NL6.





• Combined bending and membrane action.

• Presence of bifurcation.

• Initially straight elements.

• Load control.


Input Files

nlsarg07.dat

Units

SI

Material Properties

• E = 210 x 109 N/m2

• = 0.0





256 solid parabolic brick (CHEXA) elements.

Boundary Conditions

• U = V = θ = 0 at point B.

• Concentrated load at Point A applied in increments up to a value of PL2 / EI = 22.493.

Solution Type


Results

Normalizing Constants:

• EI / L2 = 170898 N

• L + 3.2 m

• = 3.14159




Graphs of results:

• X-displacement at cantilever end point vs. Load Factor.




• Y-displacement at cantilever end point vs. Load Factor

Reference

National Agency for Finite Element Methods and Standards. NAFEMS Non-Linear Benchmarks.Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.




Straight Cantilever with Axial End Point Load - BEAM Elements

This test is a nonlinear analysis of a single row of straight elements. This document provides theinput data and results for NAFEMS Non-linear Benchmarks NF6.


Input Files

nlsarp01.dat

Units

SI

Material Properties

• E = 210 x 109 N/m2

• = 0.0


32 linear (CBEAM) elements




Boundary Conditions

• U = V = θ = 0 at point B.

• Concentrated load at Point A applied in increments up to a value of PL2 / EI = 22.493 or P =–3.85 x 106 N

Solution Type


Results

Normalizing Constants:

• EI / L 2 = 170898 N

• π = 3.14159




Graphs of results:

• X-displacement at grid point 33 vs. Load Factor




• Y-displacement at grid point 33 vs. Load Factor




• Rz-displacement at grid point 33 vs. Load Factor

Reference

National Agency for Finite Element Methods and Standards, NAFEMS Non-Linear Benchmarks.Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL6.

Lee's Frame Buckling Problem

This test is a nonlinear analysis of a single row of straight elements. This document provides theinput data and results for NAFEMS Non-linear Benchmarks NF7. Attributes of this test are:





Input Files

nlsarg01.dat

Units

SI

Material Properties

• E = 71.74 x 109 N/m2

• = 0.0


20 linear beam (CBEAM) elements




Boundary Conditions

• U = V = 0; θ ≠ 0 at points B and C

• Concentrated load at Point A applied incrementally using arc-length constraint with automaticadjustment of arc length (P = –20000 N)

Solution Type





Results

Normalizing Constants EI / L2 = 996.389 N, L = 1.2 m

Graphs of results: Y-displacement at grid point 13 vs. Load Factor

Reference

National Agency for Finite Element Methods and Standards. NAFEMS Non-Linear Benchmarks.Glasgow: NAFEMS, Oct., 1989., Rev. 1. Test No. NL7.

Large Displacement Elastic Response of a Hinged Spherical Shell UnderUniform Pressure Loading

This test is a nonlinear analysis of a hinged spherical shell element under uniform pressure loading.This document provides the input data and results for A Review of Benchmark Problems forGeometric Non-Linear Behaviour of 3-D Beams and Shells (Summary) 3DNLG-7.





Input Files

nlsarg05.dat

Units

SI

Material Properties

• E = 69

• = 0.3


• The shell midsurface is defined in terms of the global Cartesian coordinate system where Z =2.0285 x 10 –4 [X (1570 – X) + Y (1570 – Y)].




Boundary Conditions

• Evenly distributed follower pressure load normal to shell surface. Maximum pressure = 0.1.Pressure follows the deformation of the shell surface.

Solution Type


• Loading method:

o Arc-length control

• Adaptive search control:

o Initial increment factor = 0.3

o Target number of iterations = 6

o Maximum number of splits = 3

o Maximum increment factor = 1

o Number of reporting steps = 18




Results

Magnitude displacement at grid point 145 vs. Load Factor

Reference

• National Agency for Finite Element Methods and Standards. A Review of Benchmark Problemsfor Geometric Non-Linear Behaviour of 3-D Beams and Shells (Summary) Glasgow: NAFEMS,Ref. R0024. Test No. 3DNLG-7



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