optistruct nonlinear response optimization

Altair Engineering – 2011

Hans Gruber – Business Development Radioss

Non-linear response optimization with OptiStruct

OptiStruct and Nonlinearities…

ContactOptiStruct 7.0

Large Displacement?

Plasticity?

Dynamic behaviour?

Complex Material models like rubber,

foam, ..?Large Sliding?

Crash?

OptiStruct and Nonlinearities…

ContactOptiStruct 7.0

Large Displacement

OptiStruct 11.0

PlasticityOptiStruct 11.0

Dynamic behaviourOptiStruct 11.0

Complex Material models like rubber,

foam, ..OptiStruct 11.0Large Sliding

OptiStruct 11.0

CrashOptiStruct 11.0

Content

� Optimization capability overview

� Solver integration

� Methods for nonlinear response optimization

� Examples

� Topology Optimization of a gear box cover (contact)

� Free shape Optimization connecting rod and a roll structure (geometric nonlinear)

� Size/Shape Optimization of a bumper (crash)

� Topology Optimization of a bumper (crash)

� Topography Optimization of a automotive door (multi body dynamics)

� Workflow (including live demo)

� Summary

Introduction - Optimization Disciplines

… generic study tool

for arbitrary solvers,

includes DOE and

Stochastics

… with integrated

FEA solver

Introduction - Optimization Disciplines

•Shape Basis Vectors

(morphing technique)

•Free Shape

•SIMP (truss)

•Free Size (shearpanel, composite)

•Continuous, Discrete

•PBARL optimization

•Shape Basis Vectors

•Beadfraction Response

OptiStruct only

Methods for Nonlinear Optimization – 10.0

Nonlinear Contact (geometric linear) � OptiStruct

� After solving the contact problem optimization is performed on a linear equation

� Sensitivity calculation wrt. design variables

Geometric Nonlinear (implicit and explicit) � HyperStudy

� Limitations

� Long calculation times (many nonlinear function calls, depending on

the number of DV)

� Topology-, Freesize, Topograhy and FreeShape Optimization are not possible

� No integrated approach

� Advantage

� Flexibility

OptiStruct

Solver integration (with optimization)

RADIOSS

FEA MBD

Geometric linear Geometric non-linear Rigid and flexible bodies

Linear:

� Static

� Dynamic

� Buckling

� Thermal

Non-linear:

� Quasi-static

� Plasticity

� Contact

Implicit:

• Quasi-static

• Dynamic

• Post-buckling

• Materials

• Contact

Explicit:

• Impact

• FSI

• Thermal

• Materials

• Contact

• Kinematic

• Dynamic

• Static

• Quasi-static

Methods for Nonlinear response optimization OptiStruct 11.0

Nonlinear Contact (NLSTAT)

� After solving the contact problem optimization is performed on a linear equation

� Sensitivity calculation wrt. design variables

Geometric Nonlinear (NLGEOM, IMPDYN, EXPDYN)

� Gradients can be very expensive or unavailable

� Transferring the nonlinear problem into a series of linear problems is

more efficient (ESLM - Equivalent static load method)

For both methods, existing optimization techniques (for linear problems) could be used

Concept of Equivalent Static Load Method

Analysis

Dynamic ProblemLoad time history

OptimizationStatic Problem

Equivalent static loads

Design variables

fteq = Kdt

• Originally developed to handle transient events (MBD) in optimization

• Modified for (geometric) nonlinear optimization

• Nonlinear implicit

• Nonlinear explicit

• Sequential static response optimization with the equivalent static loads

• Nonlinear analysis (outer loop), Static optimization (inner loop)

• will be determined in order to reach the same response

field as nonlinear analysis (including dynamic effects)

• Modified method to perform stress correction

Calculate equivalent static loads

Converged

No Yes

Update design variables Load set feq0 feq1 feq2 L feqn

Time Step t0 t1 t2 L tn time

displacement

Solve static response optimization

NonlinearAnalysis

Concept of Equivalent Static Load Method

fteq = Kdt

Questions so far?

ExamplesContact, linear Geometry, implicit solution method

Topology Optimization

Nonlinear OptimizationContact Analysis

Flange (Design Space)

ForceBearing housing

GearboxBolted flange transfers forces from housing to gearbox

Reduce mass of flange

Contact modeled between housing, flange and gearbox

Displacement Plot

Topology Optimization of a Gearbox Cover

Contact modeled

with nonlinear

GAP elements

Contact modeled

with linear spring

elements

Design Results:

Topology Optimization of a Gearbox Cover

Speedup for nonlinear sub iterations during optimization

• Gap status will be taken as initial conditions for next iteration

• Contact is solved in every optimization iteration

• Less nonlinear iterations if material distribution doesn’t change much

• Example ZF: Topology Optimization of a Gearbox Cover

• Reduction of Nonlinear iterations of about 74%

ExamplesPlastic Material, nonlinear Geometry, implicit solution method

FreeShape Optimization

Free Shape Optimization of a Connecting Rod

• Analysis Type: Geometric Non-Linearity (NLGEOM)

• Material: Johnson-Cook Elastic-Plastic Material

• Loading: Bearing Pressure (causing bending about the Z-axis)

• Problem Formulation:

• Objective Function: Minimize Volume

• Design Constraints: Element Strain ≤ 0.08

Free Shape Design Variable Grids

• With 1-plane Symmetry Manufacturing Constraint

Optimization Results – Shape

Optimization Results – Plastic Strain

Max plastic strain reduction: 0.14 to 0.007

Roll Structure Optimization

• Analysis Type: Implicit, quasi-static, nonlinear geometry

• Optimization model

Min (mass)

s.t. displacement and stress (based on requirements)

• Shape Change:

• Mass was reduced by > 16%

• 5 outer loops (nonlinear function calls)© Force India Formula One Team Ltd

Roll Structure Optimization

• Comparison final shape: nonlinear vs. linear

• Underestimation of stresses would lead to additional mass

• Additional design cycles are necessary

• One step solution with ESL

Displacements differ by 3,4% Stresses differ by 7% - 15%

ExamplesDynamic problem, nonlinear Geometry, explicit solution method

Size&Shape Optimization

Size and Shape Optimization of a Bumper

• Analysis Type: Explicit Dynamics (EXPDYN)

• Analysis Setup:

� Moving wall velocity = 2.5 m/s

� Rigid wall mass = 1000 Kg

Baseline Design Results

Optimization Formulation

• Design Variables:

� Gauge:

� Bumper backing plate: 1.5 ≤ 2.0 ≤ 3.0

� Bumper top and bottom sections: 2.0 ≤ 2.5 ≤ 3.5

� Shape

� 5 Bumper section shape variables

• Design Constraints:

� Maximum allowable mass ≤ 14 Kg

� Baseline design mass ~ 12 Kg

• Objective Function:

� Minimize bumper intrusion

Thickness design variables

Shape design variables

Objective function

Optimized Design Results

Design Comparison

Baseline Design

Backing plate thickness = 2 mmBumper sections = 2.5 mm Mass = 12 KgIntrusion = 100%

Optimized Design

Backing plate thickness = 3 mmBumper sections = 3.04 mmMass = 14 KgIntrusion = 87%

Bumper intrusion improved by ~ 13% 10 nonlinear function calls (outer loops)

ExamplesDynamic problem, nonlinear Geometry, explicit solution method

Topology Optimization

Topology Optimization of a bumber

• Introduction of rips as topology design space (connected by tied contact)

• Objective is max (d1-d2)

• S.t. m < mtarget

Topology design space inside profile Deformation due to crash loading

Optimization Results

• Objective was improved by 43%

• Mass is unchanged

Deformation before optimization Deformation after optimization

Density result

Topology Optimization of a bumber

ExamplesMulti Body Dynamics

Topography Optimization

Topography Optimization for Door Slam

*Geo Metro Model from the NHTSA website

� Objective Function:� Minimize (Max) Compliance

from the inner panel

Optimized Bead Pattern

Max Deflection under Door Slam

� ~ 19% Displacement Reduction

Current Design Optimized Design

Proposal

Topography Optimization

Results

Topography Optimization using ESLM

RADIOSS - Speed up solutions

Speedups

16 SPMD domains vs # SMP threads

1 2 3 4 5 6 7 8

#threads

RADIOSS

competitor*

Nehalem 2.80 GHz Cluster

Neon 1 million elements

8 ms simulation

� Hybrid MPP version • Hybrid version combines the benefit of booth

Radioss parallel versions SMP & SPMD inside an unique code with enhanced performance.

• Hybrid version means high flexibility : adapt to customer’s needs and hardware their resources & evolution.

• Perfect Repeatability

� Multi Domain • The global model is replaced by physically

equivalent sub domains (no limitations)

• Significant reduction of the CPU time with same accuracy

� Advanced Mass Scaling • New technology based on a modification of the

mass matrix to increase the time step

• Applicable to full models

Workflow for optimization with ESL

FEM/CAD

Models

• Unchanged workflow (vs. linear optimization)

• Analysis Model setup

• Set up of nonlinear load case(s) using bulk syntax

• Definition of the optimization model (design variables, objective,

constraints)

• ESL parameter Demo

OptiStruct

Optimization Methods

RADIOSS

FEA MBD

Geometric linear Geometric non-linear Rigid and flexible bodies

Linear:

� Static

� Dynamic

� Buckling

� Thermal

Non-linear:

� Quasi-static

� Plasticity

� Contact

Implicit:

• Quasi-static

• Dynamic

• Post-buckling

• Materials

• Contact

Explicit:

• Impact

• FSI

• Thermal

• Materials

• Contact

• Kinematic

• Dynamic

• Static

• Quasi-static

Direct sensitivities ESL

Summary – Nonlinear response optimization with OptiStruct

� OptiStruct could be applied on a wide range of nonlinear application

� All optimization disciplines are supported

� ESL is a effective and efficient approach for MBD and nonlinear

response optimization

� Various analysis solution methods are possible: quasi static/dynamic implicit or

explicit

� Integrated solver and optimization environment

� Optimization could performed on multiple load cases (MDO)

� Unchanged workflow

References

1. Altair OptiStruct, Users Manual v11.0, (2011), Altair Engineering inc., Troy MI.

2. Byung Soo Kang,YawKang Shyy, Design of Flexible Bodies in Multibody Dynamic Systems using Equivalent Static Load Method, American Institute of Aeronautics and Astronautics

3. David Mylett, Dr. Simon Gardner Force India Formula One Team Ltd., Principal Roll Structure Design Using Non-Linear Implicit Optimisation in Radioss, 7th Altair CAE Technology Conference, UK

4. Gruber H.; Schuhmacher, G.;Förtsch, C.; Rieder, E., Optimization assisted structural design of the rear fuselage of the A400M, a new military transport aircraft, *Altair Engineering, NAFEMS Seminar: “Optimization in Structural Mechanics”, April 27-28, 2005, Wiesbaden Germany

5. Hans Gruber, Warren Dias, Dennis Schwerzler, Altair Engineering; Structural Optimization in Automotive Design, automotive CAE Grand Challenge 2011, 19th – 20th March, 2011

6. Prof. Dr. Lothar Harzheim, Adam Opel AG –ITDC, The Challenge of Shape and Topology Optimization, automotive CAE Grand Challenge 2011, 19th–20thMarch, 2011

7. Ki-Jong Park and Gyung-Jin Park, Structural Optimization for Non-Linear Behavior Using Equivalent Static Loads, 16th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May - 03 June 2005, Brazil

8. Uwe Schramm, Optimization Processes for Aerospace Structures, 8th World Congress on, Structural and Multidisciplinary Optimization, June 1 - 5, 2009, Lisbon, Portugal

optistruct nonlinear response optimization

Documents

nonlinear optimization with gams /lgo

optistruct concept design using topology and topography...

optimization-driven design process - gob.mx ·...

optistruct: enabling simulation-driven innovation ·...

optimization iii convex analysis nonlinear...

nonlinear programming unconstrained optimization techniques

nonlinear trajectory optimization

case study: am pressure valve - vttresearch.com of the...

introduction to nonlinear optimization

optimization of typical kirchhoff automotive parts with...

altair optistruct 13.0 performance benchmark and...

optimization of nonlinear passive suspension

linear and nonlinear optimization - gbv

optistruct optimization 10 training manual

optimization formulation for nonlinear structural …

altair optistruct - st mühendislik · 2019. 12. 5. ·...

optistruct optimization 90 vol1 manual

optistruct optimization v2017.2 · exercise 4g: free-size...

particle swarm optimization for solving nonlinear...

nonlinear optimization techniquesappliedto combinatorial...