abaqus analysis intro book part 1 of 3

Copyright 2004 ABAQUS, Inc.

Introduction to ABAQUS/Standard and ABAQUS/Explicit



Introduction to ABAQUS/Standard and ABAQUS/Explicit 2

Day 1

Lecture 1 Defining an ABAQUS Model Workshop 1 Basic Input and Output Lecture 2 Linear Static Analysis Workshop 2 Linear Static Analysis of a Cantilever Beam:

Multiple Load Cases Lecture 3 Nonlinear Analysis in ABAQUS/Standard Workshop 3 Nonlinear Statics Lecture 4 Multistep Analysis in ABAQUS



Day 2

Lecture 5 Modeling Contact in ABAQUS Lecture 6 Contact Issues Specific to ABAQUS/Standard Workshop 4 Contact Lecture 7 Introduction to Dynamics Workshop 5 Dynamics Lecture 8 Using ABAQUS/Explicit Workshop 5 Dynamics (continued)



Day 3

Lecture 9 Contact Issues Specific to ABAQUS/Explicit Workshop 6 Contact with ABAQUS/Explicit Lecture 10 Quasi-Static Analysis in ABAQUS/Explicit Lecture 11 Combining ABAQUS/Standard and

ABAQUS/Explicit Workshop 7 Quasi-Static and Import Analysis



Additional Material

Appendix 1 Element Selection Criteria



Legal Notices

The information in this document is subject to change without notice and should not be construed as a commitment by ABAQUS, Inc.

ABAQUS, Inc., assumes no responsibility for any errors that may appear in this document.

The software described in this document is furnished under license and may be used or copied only in accordance with the terms of such license.

No part of this document may be reproduced in any form or distributed in any way without prior written agreement with ABAQUS, Inc.

Copyright ABAQUS, Inc., 2004.Printed in U.S.A.

All Rights Reserved.

ABAQUS is a registered trademark of ABAQUS, Inc.

The following are trademarks of ABAQUS, Inc.:

ABAQUS/Aqua; ABAQUS/CAE; ABAQUS/Design; ABAQUS/Explicit; ABAQUS/Foundation; ABAQUS/Standard; ABAQUS/Viewer; ABAQUS Interface for MOLDFLOW; ABAQUS Interface for MSC.ADAMS; and the ABAQUS, Inc., logo.

All other brand or product names are trademarks or registered trademarks of their respective companies or organizations.



Revision Status

Updated for v6.510/04Workshop 6

Updated for v6.510/04Lecture 11







Updated for v6.510/04Appendix 1











Updated for v6.510/04Answers 6








Defining an ABAQUS Model

Lecture 1


Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.2

Overview

Introduction Components of an ABAQUS Model Details of an ABAQUS Input File ABAQUS Input Conventions ABAQUS Output Example: Cantilever Beam Model Parts and Assemblies (optional)



Introduction



Introduction

ABAQUS, Inc. Founded in 1978.

Headquarters in Providence, Rhode Island (USA).

Offices and representatives throughout the industrialized world.

Sole activities are the development and the support of simulation software for the analysis of engineering problems.



Introduction

Headquarters: Providence, Rhode IslandBranch offices:

USA: California Indiana Michigan Ohio Rhode Island Texas

Overseas: Austria China FinlandFrance Germany (2) IndiaItaly Japan (2) KoreaNetherlands Sweden UK (2)

Representatives:Overseas: Argentina Australia Brazil

Czech Republic Malaysia New ZealandPoland Russia Singapore South Africa Spain TaiwanTurkey



Introduction

Course preliminaries This course introduces ABAQUS; basic knowledge of finite element

analysis is assumed.

This course introduces concepts in a manner that gives users a working knowledge of ABAQUS as quickly as possiblethe lecture notes do not attempt to cover all the details of ABAQUS completely.

There are several sources for additional information on the topics presented in this course:

ABAQUS Home Page (available via the Internet at www.abaqus.com). ABAQUS documentationall usage details are covered in the users

manuals.

Extensive library of lecture notes developed by ABAQUS on particular topics (a list is available at www.abaqus.com).



Introduction

ABAQUS is a suite of finite element analysis modules



Introduction

ABAQUS/CAE Complete ABAQUS Environment for

modeling, managing, and monitoring ABAQUS analyses, as well as visualizing results.

Intuitive and consistent user interface throughout the system.

Based on the concepts of parts and assemblies of part instances, which are common to many CAD systems.

Parts can be created within ABAQUS/CAE or imported from other systems as geometry (to be meshed in ABAQUS/CAE) or as meshes.

Built-in feature-based parametric modeling system for creating parts.

ABAQUS/CAE main user interface



Introduction

Solver modules ABAQUS/Standard and ABAQUS/Explicit provide the user with two

complementary analysis tools.

ABAQUS/Standards capabilities: General analyses

Static stress/displacement analysis:

Rate-independent response

Rate-dependent (viscoelastic/creep/viscoplastic) response

Transient dynamic stress/displacement analysis

Transient or steady-state heat transfer analysis

Transient or steady-state mass diffusion analysis



Introduction

Steady-state transport analysis

Coupled problems:

Thermo-mechanical (sequentially or fully coupled)

Thermo-electrical

Pore fluid flow-mechanical

Stress-mass diffusion (sequentially coupled)

Piezoelectric (linear only)

Acoustic-mechanical



Introduction

Linear perturbation analyses

Static stress/displacement analysis:

Linear static stress/displacement analysis

Eigenvalue buckling load prediction

Dynamic stress/displacement analysis:

Determination of natural modes and frequencies

Transient response via modal superposition

Steady-state response resulting from harmonic loading

Includes alternative subspace projection method for efficient analysis of large models with frequency-dependent properties (like damping)

Response spectrum analysis

Dynamic response resulting from random loading



Introduction

ABAQUS/Explicits capabilities: Explicit dynamic response with or without adiabatic heating effects

Fully coupled thermo-mechanical analysis

Structural-acoustic analysis

Annealing for multistep forming simulations

Automatic adaptive meshing allows the robust solution of highly nonlinear problems



Introduction

Comparing ABAQUS/Standard and ABAQUS/Explicit ABAQUS/Standard

A general-purpose finite element program.

Can solve for true static equilibrium in structural simulations.

Provides a large number of capabilities for analyzing many different types of problems, including many nonstructural applications.



Introduction

ABAQUS/Explicit

Solution procedure does not require iteration.

Solves highly discontinuous high-speed dynamic problems efficiently.

Does not require as much disk space as ABAQUS/Standard for larger problems.

Contact calculations are easier with ABAQUS/Explicit. Applications such as quasi-static metal forming simulations are easier.

Provides an adaptive meshing capability.



Introduction

Interactive postprocessing ABAQUS/Viewer is the

postprocessing module of ABAQUS/CAE.

Available with ABAQUS/CAE or as a stand-alone product

Can be used to visualize ABAQUS results whether or not the model was created in ABAQUS/CAE

Provides efficient visualization of large models

Contour plot of an aluminum wheel hitting a curb in ABAQUS/Viewer



Introduction

Documentation Unless otherwise indicated, all documentation is available both online

and in print.

ABAQUS Analysis Users Manual ABAQUS/CAE Users Manual ABAQUS Example Problems Manual ABAQUS Benchmarks Manual (online only) ABAQUS Verification Manual (online only) ABAQUS Theory Manual (online only)



Introduction

Additional reference materials Installation and Licensing Guide

(Installation instructions) Release Notes

(Explains changes since previous release) Advanced lecture notes on various topics (print only) Tutorials

Getting Started with ABAQUS Getting Started with ABAQUS/Standard: Keywords Version

(online only) Getting Started with ABAQUS/Explicit: Keywords Version

(online only) ABAQUS Home Pagewww.abaqus.com



Introduction

What is covered in this course Introduction to the analysis

modules and interactive postprocessing.

Details of using ABAQUS to solve a variety of structural analysis problems:

Linear Static Analysis Workshop 1: Basic Input and

Outputanalysis of forces on a connecting lug

Workshop 2: Linear Static Analysis of a Cantilever Beammultiple load cases



Introduction

Nonlinear Finite Element Analysis Workshop 3: Nonlinear Statics

large deformation analysis of a skew plate

Simulations with Several Analysis Steps

Contact among Multiple Bodies Workshop 4: Contactcontact

analysis of a plate clamped and displaced by rigid dies



Introduction

Linear and Nonlinear Dynamic Analysis Workshop 5: Dynamicsfrequency

analysis and implicit and explicit free vibration analysis of a cantilever beam

High-Speed Dynamics in ABAQUS/Explicit

Workshop 6: Contact with ABAQUS/Explicit pipe whip problem



Introduction

Quasi-Static Combined Analysis in ABAQUS/Standard and ABAQUS/Explicit

Workshop 7: Quasi-Static and Import Analysisdeep drawing of a can bottom, including springback

Nonstructural applicationssuch as heat transfer, soils consolidation, and acousticsare not discussed.

All ABAQUS analysis techniques use the same framework.

The knowledge gained in this course will help in learning to use ABAQUS for other applications.



Components of an ABAQUS Model




The ABAQUS analysis modules run as batch programs. The primary input to the analysis modules is an input file, which contains options from element, material, procedure, and loading libraries.

These options can be combined in any reasonable way, allowing a tremendous variety of problems to be modeled.

The input file is divided into two parts: model data and history data.

Model data Geometric optionsnodes, elementsMaterial optionsOther model options

History data Procedure optionsLoading optionsOutput options



Discretized model geometry

nodes,elements

Material properties


Model datadefine the physical model



v0

Fixed constraints

Initial conditions


Model data pin dof 2 fixedENCASTRE




History dataspecify what happens to the model

Types of analysis proceduresstatic, dynamic, soil, heat transfer, etc.

Loadings

Prescribed constraints

Output requestsstresses, strains, reaction forces, contact pressure, etc.

ENCASTRE

X-symmetry

Y-symmetry




History subdivided into analysis steps Steps are convenient subdivisions in an analysis history.

Different steps can contain different analysis proceduresfor example, static followed by dynamic.

Distinction between general and linear perturbation steps:

General steps define a sequence of events that follow one another.

The state of the model at the end of the previous general step provides the initial conditions for the start of the next step. This is needed for any history-dependent analysis.

Linear perturbation steps provide the linear response about the base state, which is the state at the end of the most recent general step.




Example: bow and arrow simulation

Step 1: String the bowStep 2: Pull back on the bow string Step 3: Linear perturbation step to extract the natural frequencies of the system

has no effect on subsequent stepsStep 4: Release the arrow

Step 1 = pretension Step 2 = pull back Step 4 = dynamic release

Step 3 = natural frequency extraction



Details of an ABAQUS Input File




Option blocks All data are defined in option blocks that describe specific aspects of the

problem definition, such as an element definition, etc. Together the option blocks build the model.

Node option block

Property reference option block

Material option block

Element option block

Boundary conditions option block

Contact option block

Initial conditions option block

Analysis procedure option block Loading option block

Output request option block

Model data

History data




Each option block begins with a keyword line (first character is *). Data lines, if needed, follow the keyword line. Comment lines, starting with **, can be included anywhere. All input lines have a limit of 256 characters.

Names can be up to 80 characters long and must begin with a letter. For example, the following would be a permissible name:nodes_at_the_top_of_the_block_next_to_the_gasket




Keyword lines Begin with a single * followed

directly by the name of the option.

May include a combination of required and optional parameters, along with their values, separated by commas.

Example: A material option block defines a set of material properties.

keyword

*MATERIAL, NAME=material name

parameter parameter value

The first line in a material option block




Data lines Define the bulk data for a given

option; for example, element definitions.

A keyword line may have many data lines associated with it.

Example: An element option block defines elements by specifying the element type, the element numbers, and the nodal connectivity.

*ELEMENT, TYPE=B21560, 101, 102564, 102, 103572, 103, 104

keyword line

data lines

node numbers (as required for beam B21 elements)

element numbers



*ELASTIC, TYPE=ISOTROPIC200.0E4, 0.3, 20.0150.0E3, 0.35, 400.0


Example: The elastic material option block defines the type of elasticity model as well as the elastic material properties.

keyword line

data lines

temperature

Poissons ratio

modulus of elasticity




Ordering of option blocks Each option block belongs in either the model data or the history data

one or the other as specified in the users manual.

The ordering within the model data or history data is arbitrary, except for a few cases.

Examples:

HEADING must be the first option in the input file. ELASTIC, DENSITY, and PLASTIC are suboptions of MATERIAL. As such, they must follow MATERIAL directly. Suboptions have no name references of their own.

STATIC, DYNAMIC, and FREQUENCY must follow STEP to specify the analysis procedure for the step.



Node set TOPNODEScontains nodes 101,102, ...

Boundary condition applied to all nodes in node set TOPNODES.


Node sets and element sets

Used for efficient cross referencing.

Allow you to refer to a set all at once instead of each node or element individually.

Example: Node sets*NODE, NSET=TOPNODES101, 0.345, 0.679, 0.223102, 0.331, 0.699, 0.234..*BOUNDARY, TYPE=DISPLACEMENTTOPNODES, YSYMM



Example: Element sets

*ELEMENT, TYPE=B21, ELSET=SEATPOST560, 101, 102, 564, 102, 103..*BEAM SECTION, SECTION=PIPE, MATERIAL=STEEL,ELSET=SEATPOST0.12, 0.004

pipe radius

wall thickness

These beam cross-section properties apply to all elements in element setSEATPOST.

Element set SEATPOSTcontains elements 560, 564, ...





Including data from other files ABAQUS reads data from an include file as if the data were directly in the

ABAQUS input file.

An include file can include any portion of an input file and can contain references to other include files.

Data must be in the same format as required for input file dataall rules that apply to input file syntax apply to data from included files.




Example: Input file referencing an include file

*HEADING*INCLUDE, INPUT=node_and_element_numbers.txt..

Contents of include file node_and_element_numbers.txt:*NODE, NSET=TOPNODES101, 0.345, 0.679, 0.223102, 0.331, 0.699, 0.234*ELEMENT, TYPE=B21, ELSET=SEATPOST560, 101, 102, 564, 102, 103



ABAQUS Input Conventions




Units ABAQUS uses no inherent set of units.

It is the users responsibility to use consistent units.

Example:

N, kg, m, s

or

N, 103 kg, mm, s

etc.




Time measures ABAQUS keeps track of both total time in an analysis and step time for

each analysis step.

Time is physically meaningful for some analysis procedures, such as transient dynamics.

Time is not physically meaningful for some procedures.

In rate-independent, static procedures time is just a convenient, monotonically increasing measure for incrementing loads.




Coordinate systems For input of initial nodal locations.

The default is a rectangular Cartesian system.

Specify an alternative system using SYSTEM or NODE, SYSTEM=[RECTANGULAR | CYLINDRICAL | SPHERICAL].

Do not affect loading or output because automatically converted internally to the global rectangular Cartesian system.




For nodal loads, boundary conditions, initial conditions, and output.

The default is a rectangular Cartesian system.

Specify an alternative system using the TRANSFORM option.

These directions do not rotate with the material in large-displacement analyses.

Example: Boundary conditions on a skew edge.

Use TRANSFORM on these nodes with YSYMM boundary conditions




For material point directions (directions associated with each elements material or integration points).

Affect input: Anisotropic material directions.

Affect output: Stress/strain output directions.

The default depends on the element type.

Solid elements use a global rectangular Cartesian system.

Shell and membrane elements use a projection of the global Cartesian system onto the surface.

Default material directions for shell and membrane elements

Default material directions for solid elements




Specify a local material coordinate system using the ORIENTATION option.

These directions rotatewith the material in large-displacement analyses.




Degrees of freedom Primary solution variables at the nodes.

Available nodal degrees of freedom depend on the element type.

Each degree of freedom is labeled with a number: 1=x-displacement, 2=y-displacement, ..., 11=temperature.



ABAQUS Output



ABAQUS Output

Output Four types of output are available:

Neutral binary output can be written to the output database (.odb) file using the OUTPUT option and related suboptions.

Printed output can be written to the printed output (.dat) file. This is available only for ABAQUS/Standard.

Restart output can be written to the restart (.res) file using the RESTART option for the purpose of conducting restart analyses (discussed in Lecture 4).

Results (.fil) file output can be written for third-party postprocessing.



ABAQUS Output

Output to the output database file The output database file is used by ABAQUS/Viewer. An application

programming interface (API) is available in Python and C++ to use for external postprocessing (e.g., to add data to display in ABAQUS/Viewer).

Two types of output data: field and history data.

Field data is used for model plots (deformed, contour, etc.):*OUTPUT, FIELD ABAQUS/Standard: Specify the output frequency in increments.

ABAQUS/Explicit: Specify the number of intervals during which output is written.

History data is used for XY plots:*OUTPUT, HISTORY Specify the output frequency in increments (both

ABAQUS/Standard and ABAQUS/Explicit) or the time interval between output (ABAQUS/Explicit only).



ABAQUS Output

The VARIABLE=PRESELECT parameter is optional for either history or field output. It indicates that the default output variables will be written to the output database.

Additional output variables can be selected using any of the following suboptions of OUTPUT:

NODE OUTPUTELEMENT OUTPUTENERGY OUTPUTCONTACT OUTPUTINCREMENTATION OUTPUT (ABAQUS/Explicit only)



ABAQUS Output

Output to the printed output file These options allow tabular data to be written to an ASCII file that can

be read with a text editor.

These options are available only for ABAQUS/Standard. Syntax:

*NODE PRINT*EL PRINT*ENERGY PRINT



ABAQUS Output

Output to the restart file If a simulation stops prematurely, the restart data can be used to start

the simulation from some intermediate point without repeating any calculations.

*RESTART, WRITE This option is discussed further in Lecture 4.

Output to the results file The results file can be used by third-party postprocessors.

*FILE OUTPUT (This option required for ABAQUS/Explicit only.)*NODE FILE*EL FILE*ENERGY FILE

Select specific output variables



Example: Cantilever Beam Model




Finite element model using beam elements

boundary conditions node number element number

point load



Example: Cantilever Beam Model ABAQUS input file with some annotations

Model data*HEADINGCANTILEVER BEAM EXAMPLEUNITS IN MM, N, MPa*NODE 1, 0.0, 0.0..11, 200.0, 0.0*NSET, NSET=END11,*ELEMENT, TYPE=B21, ELSET=BEAMS1, 1, 3..5, 9, 11*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150.0, 5.0** Material from XXX testing lab*MATERIAL, NAME=MAT1*ELASTIC2.0E5, 0.3*BOUNDARY1, ENCASTRE

comment line

property reference option block

heading option block

node option block

node set definition

element option block

material option block

fixed boundary condition option block

This line will appear on each page of output.

elastic option block



History data

*STEPAPPLY POINT LOAD*STATIC*CLOAD 11, 2, -1200.0*OUTPUT, FIELD, FREQUENCY=10*ELEMENT OUTPUT, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*NODE OUTPUT, NSET=ENDU*EL PRINT, FREQUENCY=10S, E*NODE FILE, FREQUENCY=5U*END STEP


The history data begin with the first *STEP option.

The history data end with the last *END STEP option.



Property references using set names*ELEMENT, TYPE=B21, ELSET=BEAMS1, 1, 3*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150.0, 5.0*MATERIAL, NAME=MAT1 *ELASTIC2.0E5, 0.3 The property reference BEAM SECTION associates the element set BEAMS with the material definition MAT1.

The option can also provide geometric information. In this case the cross-section type is rectangular (RECT); the width is 50.0; and the height is 5.0.

All elements in a model must have an appropriate property reference. Solid elements reference SOLID SECTION; shell elements reference SHELL SECTION; etc.





Material data*MATERIAL, NAME=MAT1*ELASTIC2.0E5, 0.3

Definition for an isotropic linear elastic material

ABAQUS interprets the options following a MATERIAL option as part of the same material option block until the next MATERIAL option or the next nonmaterial property option, such as the NODE option, is encountered.

Options such as ELASTIC are called suboptions and must be used in conjunction with the MATERIAL option.

Poissons ratio

elastic modulus

material name




Fixed boundary conditions*BOUNDARY1, 1, 6

Fixed boundary condition constraints are applied to active degrees of freedom.

Prescribed nonzero boundary conditions can be included only in the history data.

ABAQUS activates only the necessary degrees of freedom at a node. Thus, for this two-dimensional example with only degrees of freedom 1, 2, and 6 active, the following are equivalent input data:1, 1, 21, 6, 6or1, 1, 6or1, ENCASTRE

The batch preprocessor will issue a warning about inactive degrees of freedom.

node or node setrange of degrees of freedom or type of BC (pinned, encastre, symmetry, antisymmetry)



History definition*STEPAPPLY POINT LOAD*STATIC

The STEP option block can include a title of any length. The procedure definition must be the first option after STEP.

Begins the history data


This line appears on every page of resultsSpecifies a static analysis procedure



Loading Definition of a concentrated load in the global negative 2-direction:

*CLOAD 11, 2, -1200.0

Many distributed loadings are also available, including surface pressure, body forces, centrifugal and Coriolis loads, etc.

node or node set

degree of freedom


magnitude



Output requests

*OUTPUT, FIELD, FREQUENCY=10*ELEMENT OUTPUT, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*NODE OUTPUT, NSET=ENDU, In this case we have requested field output of a preselected set of the most

commonly used output variables.

We have also requested history output of displacements for the previously defined node set END.

Since history output is usually requested at relatively high frequencies, the sets should be as small as possible.

Each output request includes a FREQUENCY parameter. If the analysis requires many increments, the FREQUENCY parameter specifies how often results will be written to the requested file.


output to the output database file




*EL PRINT, FREQUENCY=10S, E*NODE FILE, FREQUENCY=5U Tabular output is printed to the data (.dat) file for visual inspection using

the EL PRINT option. In this case we have requested output of the stress (S) and strain (E)

components.

Binary output is written to the legacy ABAQUS results file for postprocessing in other postprocessors using the NODE FILE option.

In this case we have requested output of the displacement (U) components.

Printed output to the data file

Output to the results file



End of step

*END STEP Each analysis step ends with the END STEP option. The final option in the input file is the END STEP option for the final

analysis step.

ends the analysis step


Video Clip



Parts and Assemblies




The input file can be defined in terms of parts, part instances, and an assembly.

An ABAQUS model uses the same terminology in the input file as in ABAQUS/CAE.

Future enhancements to ABAQUS will take advantage of the concept of parts and assemblies.

Provides an inherent means of referring to distinct regions of the model. The user need not define separate sets for this purpose.

Allows reuse of part definitions, which is valuable for creating large, complex models.

Labelsnode and element numbers, set namesneed be unique only within the level in which they are defined.




Defining parts A part is defined by using the PART and END PART options, which must

appear outside of the assembly definition. Each part must have a unique name.

Defining part instances A part instance is defined by using the INSTANCE and END INSTANCE

options within the assembly definition. Each part instance must have a unique name.

Defining an assembly The assembly is defined by using the ASSEMBLY and END ASSEMBLY

options. Only one assembly can be defined in a model.

Additional sets and surfaces, as well as constraints and rigid body definitions, must appear in the assembly definition.




*HEADING...*PART, NAME=Tire

Node, element, section, set, and surface definitions*END PART*PART, NAME=Rim

Node, element, section, set, and surface definitions*END PART...*ASSEMBLY, NAME=Tire_and_rim

*INSTANCE, NAME=I_Tire, PART=Tire

set and surface definitions (optional)*END INSTANCE*INSTANCE, NAME=I_Rim, PART=Rim

set and surface definitions (optional)*END INSTANCEAdditional set and surface definitions*NSET, NSET=OutputI_Tire.514, I_Tire.520I_Rim.101, I_Rim.102

*END ASSEMBLY

...*MATERIAL, NAME=Rubber*AMPLITUDE*INITIAL CONDITIONS*PHYSICAL CONSTANTS...*STEP*STATIC

*BOUNDARYTire_and_rim.I_Rim.101, 1, 3, 0.0*CLOADTire_and_rim.I_Tire.514, 2, 1000.0

*OUTPUT, HISTORY, FREQUENCY=10*NODE OUTPUT, NSET=Tire_and_rim.OutputRF, CF

*END STEP

Example assembly input file




Node labels for parts and the assembly

node label: 101

Part: Rim

Part: Tire

node label: 514

Assembly: Tire_and_rimnode label: I_Tire.514

node label: I_Rim.101



Workshop 1: Basic Input and Output




Workshop tasks1. Use some of the ABAQUS utility programs.

2. Open the online documentation, and search for useful information.

3. Use the online documentation to determine the syntax for variousoptions.

4. Add some details to an existing input file to complete the model of a connecting lug.

50 MPa pressure load 30 kN/(2 0.015m 0.02m)




5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission).

6. View the results using ABAQUS/Viewer.

7. Become familiar with the contents of the printed output files.

8. Modify the model, and understand the changes to the results.

Video Clip



Linear Static Analysis

Lecture 2



Overview

Linear and Nonlinear Procedures Linear Static Analysis and Multiple Load Cases Multiple Load Case Usage Examples



Linear and Nonlinear Procedures




In ABAQUS/Standard there are two kinds of analysis steps:

General analysis steps:response can be linear or nonlinear.

Linear perturbation steps:response can only be linear.

Step 1 = pretension Step 2 = pull back Step 4 = dynamic release

Step 3 = natural frequency extraction

Video Clip



In this context linear analysis is a linear perturbation about a base state, which can be either the initial or the current configuration of the model.

The response prior to reaching the base state, when that is the current configuration of the model, can be nonlinear.

But the model must be in static equilibrium (the DYNAMIC option can be used only if it is followed by a STATIC step to achieve static equilibrium before the perturbation analysis is performed).

Further nonlinear analysis steps after a perturbation step are also allowed.

In ABAQUS/Explicit there are only general analysis steps.




The purely linear perturbation procedures in ABAQUS/Standard are:

BUCKLE (eigenvalue buckling analysis)FREQUENCY (eigenvalue extraction)MODAL DYNAMIC (transient linear dynamic analysis)RANDOM RESPONSE (response of structure to random excitation)RESPONSE SPECTRUM (peak linear response to dynamic loads)STEADY STATE DYNAMICS (steady-state dynamic response to

harmonic excitation)

A *STATIC step can be either a linear perturbation or a general procedure.

Discussed further in the next section.





Default amplitude references Different defaults for different

analysis procedures

AMPLITUDE=RAMP for procedureswithout natural time scales:

STATICHEAT TRANSFER, STEADY STATECOUPLED TEMPERATURE-DISPLACEMENT, STEADY STATESOILS, STEADY STATECOUPLED THERMAL-ELECTRICAL, STEADY STATESTEADY STATE TRANSPORT



AMPLITUDE=STEP for procedures with natural time scales:

DYNAMICVISCOHEAT TRANSFER (transient)COUPLED TEMPERATURE-DISPLACEMENT (transient)DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICITCOUPLED THERMAL-ELECTRICAL (transient)SOILS, CONSOLIDATIONSTEADY STATE DYNAMICSRANDOM RESPONSE MODAL DYNAMIC

A nonzero displacement boundary condition prescribed in an explicit dynamic procedure (DYNAMIC, EXPLICIT) must refer to an amplitude option.


Note: Frequency domain proceduresamplitude references define load versus frequency.



Linear Static Analysis and Multiple Load Cases



Static analyses are the only procedures that can be performed as either a general or perturbation step:

*STEP*STATICor

*STEP, PERTURBATION*STATIC

When investigating the linear static responses of a structure subjected to distinct sets of loads and boundary conditions, it is convenient (and generally more efficient) to use multiple load cases in a single perturbation step rather than using multiple perturbation steps.

A load case includes a single set of loads and boundary conditions.





Multiple load cases are advantageous when analyzing components that are subjected to many different types of loads.

Common in many industries.

For example, an aircraft experiences different loads during take-off, climb, cruise, decent, landing, and taxiing.

Each load case is applied independently.

If the stiffness of the structure is assumed constant over all phases of the loading history (linear assumption), a multiple load case analysis is an attractive option to determine the loading envelope.




Multiple *LOAD CASE Multiple STEP, PERTURBATION

Element loop(stiffness/

multiple RHS)

Primary factorization(w/ possibly multiplesmall factorizations)

Simultaneousbacksubstitution

Element loop(simultaneous

recovery)

Element loop(stiffness/

single RHS)

Factorization(or read factorized

matrix from .fct)

Backsubstitution

Element loop(recovery)

Next *STEP




Example: An agricultural implement This is an agricultural implement attached to and towed behind a tractor

through a 3-point hitch.

The purpose of the hitch is to transfer towing loads to the implement, but otherwise to allow the implement to float and move more or less independently of the tractor.




Three load cases The connection is very flexible and the loads on the implement are not well

defined, but are a combination of many different types of loads.

Vertical Loads

Lateral Loads

Forward Loads



Multiple Load Case Usage




The following procedures support load cases:

*STEP, PERTURBATION*STATIC

*STEADY STATE DYNAMICS, DIRECT A load case may contain the following load types:

Concentrated and distributed loads

Boundary conditions (may change from load case to load case)

Inertia relief




...*Step, perturbation*Static*Load Case, name="Bending A"*Boundaryright, 1, 6*Cloadleft, 3, 1.*End Load Case *Load Case, name="Bending B"*Boundaryleft, 1, 6*Cloadright, 3, 1.*End Load Case*End Step

Node set left

Node set right

Bending A

Bending B




Additional rules Load case names (LOAD CASE, name=name) must be unique Load options specified outside of load cases apply to all load cases

Base state boundary conditions propagate to all load cases Rules for using OP=NEW

If used anywhere in a load case step, must be used everywhere inthat step

If used on any BOUNDARY in a load case step, propagated boundary conditions will be removed in all load cases

LOAD CASE options do not propagate




Changing boundary conditions from load case to load case No performance penalty when boundary conditions change only in

magnitude.

Limit number of boundary conditions which change location from load case to load case.

Depending on number and distribution of boundary conditions which change location, multiple load case analysis may be significantly slower than equivalent multiple step analysis (very problem dependent).

If in doubt, run datacheck analyses (multiple step vs. multiple load case) and compare solver information in data (.dat) file (e.g., memory requirements, number of floating point operations, etc.).




Problem size Combination of number of degrees of freedom and number of load cases

determines problem size.

Multiple load case analyses may require more:

memory than equivalent multiple step analyses (e.g., all right-hand-sides must be kept in core during backsubstitution).

disk space (element and nodal databases).

When possible, set: standard_memory to minimize I/O (see data file). standard_memory_policy to MAXIMUM.

If necessary, spread load cases over several steps to reduce memory/disk usage per step.

Worst case: resort to multiple perturbation steps (again, compare solver information in data file).




Output Output requested per step (not per

load case)

Available for the output database (.odb) and printed output (.dat) files

For the output database file:

All output variables for a load case are mapped to a frame

Similar to the way increments are mapped to frames

Frame contains load case name

Field output only (no history output)




Postprocessing with ABAQUS/Viewer

Operations on entire frames supported

For selected frames, can create:

Linear combinations (e.g., linear combination of load cases)

Min/Max envelope (e.g., find max stresses over all load cases)




Mises stress: Bending A Mises stress: Bending B

Max value of Mises stress over both frames



Examples



Examples

Square plate benchmark

Number of load cases: 8 and 16 *Static, perturbation Changing boundary condition

locations at corners

Default output

Changing BCs15060065013

2424062012

33840067514

612061011

# variables(# DOF)# nodes/edgeModel



Examples

Performance results: Total CPU time

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

0.E+00 1.E+06 2.E+06 3.E+06 4.E+06Number of variables

CPU

time

(sec

)

8 Steps8 Load Cases16 Steps16 Load Cases



Examples

Performance: Details for 751 751 model

Relative CPU Time 3.4 M variable case

7.485.04Total

14.37.52Solver

16 Steps/16 Load cases8 Steps/8 Load cases



Examples

Modify 501 501 model 8 load cases

Boundary conditions on opposite edges changing per load case

Relative total CPU time: ~0.153 (multiple load case ~6.6 slower!)

Watch number and location of changing boundary conditions!

Changing BCs



Examples

Chassis-bracket mobility analysis:Number of variables: 534,000

Number of equations: 483,000

Number of load cases: 60*Steady-state dynamics, direct

(10 frequency points)

Output: U (output database)

CPU time (sec)

11,600 (10 faster)1965 60 = 117,600Total1990 (39 faster)1290 60 = 77,400Solver

60 load cases60 steps (projected based on 1 step)



Workshop 2: Linear Static Analysis of a Cantilever Beam



Workshop 2: Linear Static Analysis of a Cantilever Beam

Workshop tasks1. Use multiple load cases to analyze the bending response of the beam.

2. Compare the solution and analysis times obtained using a single step with multiple load cases and multiple steps with single load cases.



Nonlinear Analysis in ABAQUS/Standard

Lecture 3



Overview

Nonlinearity in Structural Mechanics Solving Equilibrium Equations Nonlinear Input File Output from Nonlinear Cantilever Beam Analysis



Nonlinearity in Structural Mechanics




Some examples of material nonlinearity

Sources of nonlinearity Material nonlinearities:

Nonlinear elasticity

Plasticity

Material damage

Failure mechanisms

Etc.

Note: Material dependencies on temperature or field variables do not introduce nonlinearity if the temperature or field variables are predefined.




An example of self-contact:Example Problem 1.1.16, Compression of a jounce bumper

Boundary nonlinearities: Contact problems

Boundary conditions change during the analysis.

Extremely discontinuous form of nonlinearity.

Video Clip




Geometric nonlinearities: Large deflections and

deformations

Large rotations

Structural instabilities (buckling)

Preloading effects

An example of geometric nonlinearity: elastomeric keyboard dome

Video Clip



Solving Equilibrium Equations




Typical nonlinear problems have all three forms of nonlinearity.

Must include the nonlinear terms in the equations.

Generally, the nonlinear equations for each degree of freedom are coupled.

The basic statement of static equilibrium is that the internal forces exerted on the nodes, I, resulting from the element stresses and external forces, P, acting at every node must balance:

0)()( = uIuP (Eq. 3.1)







To solve for equilibrium in nonlinear problems, ABAQUS/Standard uses an incremental-iterative solution, based on the Newton-Raphson technique.

Assume that the solution to the previous load increment, u0, is known.

Assume that after an iteration, i, an approximation, ui, to the solution has been obtained. Let ci+1 be the difference between this solution and the exact solution to the discrete equilibrium equation, Equation 3.1, so that

Expanding the left-hand side of Equation 3.2 in a Taylor series about the approximate solution, ui, then gives

(Eq. 3.2)

(Eq. 3.3)

.0)()( 11 =++ ++ iiii cuIcuP

1( ) ( )( ) ( ) .... 0i ii i i

P u I uP u I u cu u +

+ + = .



By ignoring higher-order terms, the equation can be written as

where is the tangent stiffness.

The next approximation to the solution is

Note that if the load depends on displacement (e.g., pressure on a surface that rotates), the stiffness matrix includes a load stiffness contribution.


,)()(1 iiii uIuPcK =+

uuP

uuIK iii

= )()(

.11 ++ += iii cuu




Static equilibrium in a mesh1. Apply an increment of

prescribed load.

2. Iterate until the sum of all forces acting on each node is small.

3. Update the state once equilibrium has been satisfied.

4. Go back to Step 1, and apply the next load increment.



Single degree of freedom example

Nonlinear spring

Find u(P) or P(u)typically, load ramped from 0 to PFINALduring the step.

Time will usually vary from 0 to 1.





Newton-Raphson solution technique

Iteration 1 (i=1) Assume that the solution u0, P0

at the end of the previous converged increment is known.

A small increment of load, P, is applied to the structure during the current increment.

ABAQUS determines the displacement correction, c1, based on the tangent stiffness,K0, at u0; the total load, PTOTAL; and the internal forces at the end of the previous increment,

.: 0100 IPcKI TOTAL =



ABAQUS forms K1 and calculates I1 based on the updated state of the model, u1.

The difference between the total applied force, PTOTAL, and the internal force, I1, is called the force residual, R1: R1= PTOTAL I1.

If R1 is very small (within the tolerance limit) at every degree of freedom in the model, the structure is in equilibrium.

The default tolerance is that R1 must be less than 0.5% of the time averaged force in the structure.

ABAQUS automatically calculates the time averaged force.

If the iteration does not produce a converged solution, ABAQUS will perform another iteration in an attempt to find a converged solution.




Iteration 2 (i=2) A new displacement

correction, c2, is calculated based on the updated stiffness, K1, and

The new residual, R2, is compared with the tolerances to see if the solution, u2, is converged.


.1211 : IPcKI TOTAL =




This procedure is repeated until force residuals are within the tolerance limits. Each iteration, i, requires:

1. Formulation of tangent stiffness, Ki.

2. Solution of simultaneous system of equations for ci+1.

Update the estimate of the solution: ui+1 = ui + ci+1.

3. Calculation of internal force vector Ii+1 based on ui+1.4. Judgment of equilibrium convergence:

Is Ri+1 within the tolerance?

Is#

11

iter

i jj

c c+=



Nonlinear Input File




*HEADINGCANTILEVER BEAM EXAMPLE--LARGE DISPLACEMENT*NODE 1, 0., 0.11, 200., 0.*NGEN1, 11, 1*ELEMENT, TYPE=B211, 1, 3*ELGEN, ELSET=BEAMS1, 5, 2, 1*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150., 5.*MATERIAL, NAME=MAT1*ELASTIC2.E5, .3*BOUNDARY1, 1, 6*AMPLITUDE, NAME=RAMP0.0, 0.0, 0.5, 0.3, 1.0, 1.0



*RESTART, WRITE,FREQ=3*STEP, NLGEOM,INC=25APPLY POINT LOAD*STATIC0.1, 1.0, 0.001, 1.0*CLOAD, AMPLITUDE=RAMP11, 2, -1200. *NODE PRINT, FREQ=1U, RF*EL PRINT, FREQ=10S, E*NODE FILE, FREQ=5U*END STEP

major differences from linear input

minimum time increment

maximum time increment

time period of the step

initial suggested time increment

previously defined amplitude function for load application

major differences from linear input




Step and procedure input

*STEP, NLGEOM, INC=25 NLGEOM: include all nonlinear geometric effects due to:

Large deflections, rotations, deformation.

Preloading (initial stresses).

Load stiffness.

If the above are not important, the answer will be the same as without NLGEOM but the analysis will be more expensive.

INC=25: maximum of 25 increments allowed in this example:

The code will stop if the maximum number of increments is reached before the total load is applied.

Keeps the analysis from running too longyou can always restart.

Default value is 100.





Similar time incrementation data exist for all transient procedures, which are

STATICDYNAMICHEAT TRANSFERVISCOCOUPLED TEMPERATURE-DISPLACEMENTSOILSMODAL DYNAMIC (allows only fixed time incrementation)COUPLED THERMAL-ELECTRIC

Physical or normalized time scale depending on the procedure and the presence of time-dependent or rate-dependent behavior.



Output from Nonlinear Cantilever Beam Analysis




Status (.sta) file Summarizes how analysis proceedsshows automatic time

incrementation at work.

You can check the status file while the job is running.

One line written after each successful increment.

SUMMARY OF JOB INFORMATION:STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF

DISCON ITERS ITERS TIME/ TIME/LPF TIME/LPF MONITOR RIKSITERS FREQ

1 1 1 0 3 3 0.100 0.100 0.1000 1 2 1 0 2 2 0.200 0.200 0.1000 1 3 1 0 2 2 0.350 0.350 0.1500 1 4 1 0 2 2 0.575 0.575 0.2250 1 5 1 0 4 4 0.913 0.913 0.3375 1 6 1 0 2 2 1.00 1.00 0.08750



Automatic time incrementation Heuristic algorithm (based on many years of experience) controls the

accuracy of time integration. In statics based on number of iterations to converge.

Convergence is easily achieved (considerably less than the maximum number of allowable iterations):

increase increment size Convergence difficult or divergence occurs:

cut back increment size Otherwise:

maintain same increment size Automatic time incrementation works very well. The user should not

change it without good reason.Tip: For highly nonlinear problems, it is recommended that the initial time increment be chosen as a small fraction (e.g., 10%) of the total step time.




Message (.msg) file Includes:

All convergence controls:

The CONTROLS option overrides defaultsnot usually needed Details about certain model features:

Nondefault model features

Use of NLGEOM

Frequency of restart writes

All iteration details





Solver messages:

Numerical singularities: These indicate that so many digits are lost during linear equation solution that the results are not reliable. The most common cause is an unconstrained rigidbody mode in a static stress analysis.

Zero pivots: These occur during linear equation solution when there is a force term but nocorresponding stiffness. Common causesare unconstrained rigid body modes and overconstrained degrees of freedom.

Negative eigenvalues: Negative eigenvalues indicate that the stiffness matrix is not positive definite; for example, a buckling load may have been exceeded.




Useful troubleshooting information:

Locations of highest residuals

Locations of excessive deformation

Locations of contact changes



S T E P 1 S T A T I C A N A L Y S I S

APPLY POINT LOADAUTOMATIC TIME CONTROL WITH -

A SUGGESTED INITIAL TIME INCREMENT OF 0.100 AND A TOTAL TIME PERIOD OF 1.00 THE MINIMUM TIME INCREMENT ALLOWED IS 1.000E-03THE MAXIMUM TIME INCREMENT ALLOWED IS 1.00

CONVERGENCE TOLERANCE PARAMETERS FOR FORCE CRITERION FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 5.000E-03CRITERION FOR DISP. CORRECTION IN A NONLINEAR PROBLEM 1.000E-02INITIAL VALUE OF TIME AVERAGE FORCE 1.000E-02AVERAGE FORCE IS TIME AVERAGE FORCE ALTERNATE CRIT. FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 2.000E-02CRITERION FOR ZERO FORCE RELATIVE TO TIME AVRG. FORCE 1.000E-05CRITERION FOR RESIDUAL FORCE WHEN THERE IS ZERO FLUX 1.000E-05CRITERION FOR DISP. CORRECTION WHEN THERE IS ZERO FLUX 1.000E-03CRITERION FOR RESIDUAL FORCE FOR A LINEAR INCREMENT 1.000E-08FIELD CONVERSION RATIO 1.00




CONVERGENCE TOLERANCE PARAMETERS FOR MOMENT CRITERION FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 5.000E-03CRITERION FOR ROTATION CORRECTION IN A NONLINEAR PROBLEM 1.000E-02INITIAL VALUE OF TIME AVERAGE MOMENT 1.000E-02AVERAGE MOMENT IS TIME AVERAGE MOMENT ALTERNATE CRIT. FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 2.000E-02CRITERION FOR ZERO MOMENT RELATIVE TO TIME AVRG. MOMENT 1.000E-05CRITERION FOR RESIDUAL MOMENT WHEN THERE IS ZERO FLUX 1.000E-05CRITERION FOR ROTATION CORRECTION WHEN THERE IS ZERO FLUX 1.000E-03CRITERION FOR RESIDUAL MOMENT FOR A LINEAR INCREMENT 1.000E-08FIELD CONVERSION RATIO 1.00

VOLUMETRIC STRAIN COMPATIBILITY TOLERANCE FOR HYBRID SOLIDS 1.000E-05AXIAL STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1.000E-05TRANS. SHEAR STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1.000E-05SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P>P0 5.000E-03SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P=0.0 0.100 DISPLACEMENT COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1.000E-05ROTATION COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1.000E-05




TIME INCREMENTATION CONTROL PARAMETERS:FIRST EQUILIBRIUM ITERATION FOR CONSECUTIVE DIVERGENCE CHECK 4EQUILIBRIUM ITERATION AT WHICH LOG. CONVERGENCE RATE CHECK BEGINS 8EQUILIBRIUM ITERATION AFTER WHICH ALTERNATE RESIDUAL IS USED 9MAXIMUM EQUILIBRIUM ITERATIONS ALLOWED 16EQUILIBRIUM ITERATION COUNT FOR CUT-BACK IN NEXT INCREMENT 10MAXIMUM EQUILIB. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 4MAXIMUM ITERATIONS FOR SEVERE DISCONTINUITIES 12MAXIMUM CUT-BACKS ALLOWED IN AN INCREMENT 5MAXIMUM DISCON. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 6CUT-BACK FACTOR AFTER DIVERGENCE 0.2500 CUT-BACK FACTOR FOR TOO SLOW CONVERGENCE 0.5000 CUT-BACK FACTOR AFTER TOO MANY EQUILIBRIUM ITERATIONS 0.7500 CUT-BACK FACTOR AFTER TOO MANY SEVERE DISCONTINUITY ITERATIONS 0.2500 CUT-BACK FACTOR AFTER PROBLEMS IN ELEMENT ASSEMBLY 0.2500 INCREASE FACTOR AFTER TWO INCREMENTS THAT CONVERGE QUICKLY 1.500MAX. TIME INCREMENT INCREASE FACTOR ALLOWED 1.500 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DYNAMICS) 1.250 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DIFFUSION) 2.000 MINIMUM TIME INCREMENT RATIO FOR EXTRAPOLATION TO OCCUR 0.1000 MAX. RATIO OF TIME INCREMENT TO STABILITY LIMIT 1.000 FRACTION OF STABILITY LIMIT FOR NEW TIME INCREMENT 0.9500




PRINT OF INCREMENT NUMBER, TIME, ETC., EVERY 1 INCREMENTS

RESTART FILE WILL BE WRITTEN EVERY 3 INCREMENTSTHE MAXIMUM NUMBER OF INCREMENTS IN THIS STEP IS 25

LARGE DISPLACEMENT THEORY WILL BE USEDLINEAR EXTRAPOLATION WILL BE USEDCHARACTERISTIC ELEMENT LENGTH 40.0 DETAILED OUTPUT OF DIAGNOSTICS TO DATABASE REQUESTEDPRINT OF INCREMENT NUMBER, TIME, ETC., TO THE MESSAGE FILE EVERY 1 INCREMENTSEQUATIONS ARE BEING REORDERED TO MINIMIZE WAVEFRONTCOLLECTING MODEL CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKSCOLLECTING STEP CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKS




Output from Nonlinear Cantilever Beam AnalysisINCREMENT 1 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.100

EQUILIBRIUM ITERATION 1AVERAGE FORCE 1.251E+03 TIME AVG. FORCE 1.251E+03LARGEST RESIDUAL FORCE -4.637E+03 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.84 AT NODE 11 DOF 2

FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT 28.8 AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.382E-02 AT NODE 11 DOF 6

MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.EQUILIBRIUM ITERATION 2

AVERAGE FORCE 37.8 TIME AVG. FORCE 37.8 LARGEST RESIDUAL FORCE 0.215 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.007E-02 AT NODE 11 DOF 1

FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT -0.346 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.898E-07 AT NODE 11 DOF 6

THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED

0.005

6.25

0.005

0.2

0.005

36

0.005

36



EQUILIBRIUM ITERATION 3

AVERAGE FORCE 37.7 TIME AVG. FORCE 37.7 LARGEST RESIDUAL FORCE -2.281E-06 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 3.349E-05 AT NODE 11 DOF 2

THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT 1.523E-05 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 3.637E-07 AT NODE 11 DOF 6

THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDITERATION SUMMARY FOR THE INCREMENT: 3 TOTAL ITERATIONS, OF WHICH

0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS.TIME INCREMENT COMPLETED 0.100 , FRACTION OF STEP COMPLETED 0.100 STEP TIME COMPLETED 0.100 , TOTAL TIME COMPLETED 0.100


4 or fewer iterations (do this again and t can increase)

0.005

0.2

0.005

36



INCREMENT 2 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.100EQUILIBRIUM ITERATION 1

AVERAGE FORCE 75.6 TIME AVG. FORCE 56.7 LARGEST RESIDUAL FORCE 0.861 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -2.013E-02 AT NODE 11 DOF 1




no increase



EQUILIBRIUM ITERATION 2AVERAGE FORCE 144. TIME AVG. FORCE 90.9 LARGEST RESIDUAL FORCE -6.928E-05 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 1.701E-04 AT NODE 11 DOF 2


THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDTIME INCREMENT MAY NOW INCREASE TO 0.150

ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.

TIME INCREMENT COMPLETED 0.100 , FRACTION OF STEP COMPLETED 0.200 STEP TIME COMPLETED 0.200 , TOTAL TIME COMPLETED 0.200


4 consecutive increments with 4 or fewer iterations: t = 1.5told




AVERAGE FORCE 133. TIME AVG. FORCE 105. LARGEST RESIDUAL FORCE 3.02 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -2.75 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -3.764E-02 AT NODE 11 DOF 1




t = 1.5told



EQUILIBRIUM ITERATION 2

AVERAGE FORCE 252. TIME AVG. FORCE 145. LARGEST RESIDUAL FORCE -7.965E-04 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -2.75 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 5.629E-04 AT NODE 11 DOF 2





RESTART INFORMATION WRITTEN IN STEP 1 AFTER INCREMENT 3


4 or fewer



INCREMENT 4 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.225 EQUILIBRIUM ITERATION 1

AVERAGE FORCE 1.528E+03 TIME AVG. FORCE 490. LARGEST RESIDUAL FORCE -4.550E+03 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -5.95 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.82 AT NODE 11 DOF 2

FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 4.853E+04 TIME AVG. MOMENT 2.493E+04LARGEST RESIDUAL MOMENT -344. AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -4.477E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.371E-02 AT NODE 11 DOF 6

MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.


t = 1.5told



EQUILIBRIUM ITERATION 2AVERAGE FORCE 281. TIME AVG. FORCE 179. LARGEST RESIDUAL FORCE 0.349 AT NODE 11 DOF 2LARGEST INCREMENT OF DISP. -5.94 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -9.348E-03 AT NODE 11 DOF 1

THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 4.847E+04 TIME AVG. MOMENT 2.491E+04LARGEST RESIDUAL MOMENT -2.26 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -4.471E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.353E-05 AT NODE 11 DOF 6








AVERAGE FORCE 1.248E+04 TIME AVG. FORCE 2.638E+03LARGEST RESIDUAL FORCE -3.911E+04 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.2 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -5.31 AT NODE 11 DOF 2FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.049E+05 TIME AVG. MOMENT 4.090E+04LARGEST RESIDUAL MOMENT -4.323E+03 AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -0.107 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -4.037E-02 AT NODE 11 DOF 6MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

EQUILIBRIUM ITERATION 2AVERAGE FORCE 556. TIME AVG. FORCE 254. LARGEST RESIDUAL FORCE 16.6 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.2 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -8.119E-02 AT NODE 11 DOF 1FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.044E+05 TIME AVG. MOMENT 4.080E+04LARGEST RESIDUAL MOMENT -42.5 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -0.107 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.095E-04 AT NODE 11 DOF 6THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED


t = 1.5told



EQUILIBRIUM ITERATION 3AVERAGE FORCE 559. TIME AVG. FORCE 255. LARGEST RESIDUAL FORCE -28.9 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.1 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 0.130 AT NODE 11 DOF 2FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.

AVERAGE MOMENT 1.153E+05 TIME AVG. MOMENT 4.299E+04LARGEST RESIDUAL MOMENT 3.833E-02 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -0.106 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.112E-03 AT NODE 11 DOF 6ESTIMATE OF ROTATION CORRECTION -1.004E-06MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTIONEQUILIBRIUM ITERATION 4

AVERAGE FORCE 1.053E+03 TIME AVG. FORCE 354. LARGEST RESIDUAL FORCE 1.092E-03 AT NODE 11 DOF 2LARGEST INCREMENT OF DISP. -14.1 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -2.092E-04 AT NODE 11 DOF 2THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 1.153E+05 TIME AVG. MOMENT 4.299E+04LARGEST RESIDUAL MOMENT -2.910E-02 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -0.106 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.875E-06 AT NODE 11 DOF 6

THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDITERATION SUMMARY FOR THE INCREMENT: 3 TOTAL ITERATIONS, OF WHICH

0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS.TIME INCREMENT COMPLETED 0.338 , FRACTION OF STEP COMPLETED 0.913 STEP TIME COMPLETED 0.913 , TOTAL TIME COMPLETED 0.913


The residual is within tolerance, but the rotation correction is too large. The estimate of the rotation correction of the next iteration is acceptably small.



INCREMENT 6 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 8.750E-02EQUILIBRIUM ITERATION 1

AVERAGE FORCE 641. TIME AVG. FORCE 402. LARGEST RESIDUAL FORCE 74.0 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -3.55 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -0.180 AT NODE 11 DOF 1

FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.179E+05 TIME AVG. MOMENT 5.547E+04LARGEST RESIDUAL MOMENT -99.4 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -2.702E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.186E-04 AT NODE 11 DOF 6ESTIMATE OF ROTATION CORRECTION -1.594E-05MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTION

EQUILIBRIUM ITERATION 2AVERAGE FORCE 695. TIME AVG. FORCE 411. LARGEST RESIDUAL FORCE -0.505 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -3.53 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 1.386E-02 AT NODE 11 DOF 2







TIME INCREMENT COMPLETED 8.750E-02, FRACTION OF STEP COMPLETED 1.00 STEP TIME COMPLETED 1.00 , TOTAL TIME COMPLETED 1.00

RESTART INFORMATION WRITTEN IN STEP 1 AFTER INCREMENT 6

THE ANALYSIS HAS BEEN COMPLETED

ANALYSIS SUMMARY:TOTAL OF 6 INCREMENTS

0 CUTBACKS IN AUTOMATIC INCREMENTATION15 ITERATIONS INCLUDING CONTACT ITERATIONS IF PRESENT15 PASSES THROUGH THE EQUATION SOLVER OF WHICH 15 INVOLVE MATRIX DECOMPOSITION, INCLUDING0 DECOMPOSITION(S) OF THE MASS MATRIX1 REORDERING OF EQUATIONS TO MINIMIZE WAVEFRONT0 ADDITIONAL RESIDUAL EVALUATIONS FOR LINE SEARCHES0 ADDITIONAL OPERATOR EVALUATIONS FOR LINE SEARCHES3 WARNING MESSAGES DURING USER INPUT PROCESSING0 WARNING MESSAGES DURING ANALYSIS0 ANALYSIS WARNINGS ARE NUMERICAL PROBLEM MESSAGES0 ANALYSIS WARNINGS ARE NEGATIVE EIGENVALUE MESSAGES0 ERROR MESSAGES


Look here for warning and error messages. Search the message file and data file to determine the causes of these messages.




Visual diagnostics in ABAQUS/Viewer

Toggle on to see the locations in the model where the largest residuals and displacement increments and corrections occur.

A similar display is given for rotational degrees of freedom



Workshop 3: Nonlinear Statics



Workshop 3: Nonlinear Statics

Workshop tasks1. Define alternate material

directions correspondingto the skew angle of the plate.

2. Analyze the deformation of the skew plate with and without considering nonlinear geometric effects.

3. Include plasticity in the material definition.

4. View the results using ABAQUS/Viewer.

Video Clip



Multistep Analysis in ABAQUS

Lecture 4



Overview

Multistep Analyses Restart Analysis in ABAQUS



Multistep Analyses



Multistep Analyses

It is often convenient to divid

abaqus analysis intro book part 1 of 3

Documents