Optistruct Nonlinear Response optimization

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

Non-linear response optimization with OptiStruct Altair Altair Engineeri Engineering ng – 2011 Hans Gruber Gruber – Business Business Developmen Developmentt Radioss Radioss


OptiSt Opt iStruc ructt and Nonlinea Nonlinearit rities ies… …

Plasticity? Contact Opti Op tiSt Stru ruct ct 7. 7.0 0

Large Sliding?

Com ompl plex ex Ma Mate teri rial al models like rubber, foam, ..?

Dynamic behaviour?

Large Displacement? Crash?



Plasticity? Contact Opti Op tiSt Stru ruct ct 7. 7.0 0

Large Sliding?

Com ompl plex ex Ma Mate teri rial al models like rubber, foam, ..?

Dynamic behaviour?

Large Displacement? Crash?



Plasticity Opti Op tiSt Stru ruct ct 11. 11.0 0

Contact Opti Op tiSt Stru ruct ct 7. 7.0 0

Large Sliding

Com ompl plex ex Ma Mate teri rial al models like rubber, foam, .. Opti Op tiSt Stru ruct ct 11 11.0 .0

Opti Op tiSt Stru ruct ct 11. 11.0 0

Dynamic behaviour

Large Displacement

Opti Op tiSt Stru ruct ct 11. 11.0 0

Opti Op tiSt Stru ruct ct 11 11.0 .0

Crash Opti Op tiSt Stru ruct ct 11 11.0 .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

… with integrated FEA solver

… generic study tool for arbitrary solvers, includes DOE and Stochastics


Introduction - Optimization Disciplines

•SIMP (truss)

•Shape Basis Vectors

•Free Size (shear panel, composite)

(morphing technique)

•Shape Basis Vectors

•Continuous, Discrete

•Beadfraction Response

•PBARL optimization

•Free Shape

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


Solver integration (with optimization)

OptiStruct RADIOSS FEA

MBD

Geometric linear

Geometric non-linear

Rigid and flexible bodies

Linear:

Implicit:

Explicit:

• Kinematic

Non-linear:



Static



Quasi-static

• Quasi-static

• Impact

• Dynamic



Dynamic



Plasticity

• Dynamic

• FSI

• Static



Buckling



Contact

• Post-buckling

• Thermal

• Quasi-static



Thermal

• Materials

• Materials

• Contact

• Contact


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 Problem Load time history

d

Optimization Static Problem

Load

Design variables

Equivalent static loads

ft eq = Kdt t

• Originally developed to handle transient events (MBD) in optimization • Modified for (geometric) nonlinear optimization • Nonlinear implicit • Nonlinear explicit


Concept of Equivalent Static Load Method • Sequential static response optimization with the equivalent static loads • Nonlinear analysis (outer loop), Static optimization (inner loop) •

ft eq = Kdt will be determined in order to reach the same response

field as nonlinear analysis (including dynamic effects) • Modified method to perform stress correction Start Nonlinear Analysis

displacement

Calculate equivalent static loads

Update design variables

Time Step t0 t1 t2 L Load set

Solve static response optimization

No

f eq0 f eq1 f eq2 L

tn time f eqn

Yes Converged

Stop

Questions so far?


Examples Contact, linear Geometry, implicit solution method Topology Optimization


Nonlinear Optimization Contact Analysis Topology Optimization of a Gearbox Cover

Bolted flange transfers forces from housing to gearbox

Flange (Design Space)

Gearbox

Reduce mass of flange Contact modeled between housing, flange and gearbox

Displacement Plot

Force Bearing housing


Nonlinear Optimization Contact Analysis Topology Optimization of a Gearbox Cover Design Results:

Contact modeled with linear spring elements

Contact modeled with nonlinear GAP elements


Nonlinear Optimization Contact Analysis

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%


Examples Plastic 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

Displacements differ by 3,4%

Stresses differ by 7% - 15%

• Underestimation of stresses would lead to additional mass • Additional design cycles are necessary • One step solution with ESL

© Force India Formula One Team Ltd


Examples Dynamic 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


Size and Shape Optimization of a Bumper 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 

Thickness design variables

5 Bumper section shape variables

• Design Constraints: 

Maximum allowable mass ≤ 14 Kg



Baseline design mass ~ 12 Kg

• Objective Function: 

Shape design variables

Minimize bumper intrusion

Objective function


Size and Shape Optimization of a Bumper Optimized Design Results


Design Comparison

Baseline Design

Optimized Design

Backing plate thickness = 2 mm Bumper sections = 2.5 mm Mass = 12 Kg Intrusion = 100%

Backing plate thickness = 3 mm Bumper sections = 3.04 mm Mass = 14 Kg Intrusion = 87%

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


Examples Dynamic 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


Topology Optimization of a bumber Optimization Results • Objective was improved by 43% • Mass is unchanged

Density result

Deformation before optimization

Deformation after optimization


Examples Multi Body Dynamics Topography Optimization


Topography Optimization for Door Slam



Objective Function: 

*Geo Metro Model from the NHTSA website

Minimize (Max) Compliance from the inner panel


Optimized Bead Pattern

*Geo Metro Model from the NHTSA website


Max Deflection under Door Slam



~ 19% Displacement Reduction *Geo Metro Model from the NHTSA website


Topography Optimization using ESLM

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RADIOSS - Speed up solutions 

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

Nehalem 2.80 GHz Cluster Neon 1 million elements Speedups 16 SPMD domains vs # SMP threads

8 ms simulation



Advanced Mass Scaling • •

New technology based on a modification of the mass matrix to increase the time step Applicable to full models

6

5,08 5

s p4 u d e e3 p S

3,65

1

2,9

1,95

2

3,8

RADIOSS competitor*

1,88

11

1

2

3

4

5

#threads

6

7

8


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


Optimization Methods OptiStruct RADIOSS FEA

MBD

Geometric linear

Geometric non-linear

Rigid and flexible bodies

Linear:

Implicit:

Explicit:

• Kinematic

Non-linear:



Static



Quasi-static

• Quasi-static

• Impact

• Dynamic



Dynamic



Plasticity

• Dynamic

• FSI

• Static



Buckling



Contact

• Post-buckling

• Thermal

• Quasi-static



Thermal

• Materials

• Materials

• Contact

• Contact

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

Optistruct Nonlinear Response optimization

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