optistruct nonlinear response optimization

Copyright © 2011 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.

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

Load

Design variables

fteq = Kdt

t

d

• 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

Start

Calculate equivalent static loads

Converged

No Yes

Stop

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%

© Force India Formula One Team Ltd


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

1,88

1

1,95

3,65

5,08

2,9

3,8

1

2

3

4

5

6

1 2 3 4 5 6 7 8

#threads

Sp

ee

du

ps

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

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