Topology Optimizationwith PERMAS

Reinhard HelfrichINTES GmbHJune 2002

INTES

• FEA technology since 1984

• Development of PERMAS, a general purpose FEanalysis system (statics, dynamics, acoustics,thermodynamics, electrodynamics, optimization)

• Development of new and efficient numericalmethods (parallelization, optimization, stochasticFEA)

• All services around PERMAS (training, hotline,analysis projects)

Layout optimization is a valuable tool to get conceptual ideasin the early development phase of structural parts.

•Design space specification with free and fixed parts

•Provide boundary conditions

•Provide loads

•Target definition with remaining volume

Free and fixed design elements

• Selection of filling ratio per design element

• Limits for design elements

• Limits on design variable modification

Design objective

• Compliance

• Vibration frequency (range)

Multimodeling

• Several loading cases simultaneously with different options forsuperposition

• Different design variants

Modeling

Analysis

Options

• Linear statics

• Contact analysis

• Dynamic mode analysis

Algorithms for optimization

• Method of moving asymptotes (MMA) with dual oroptimality criteria

• Polynomial approach with dual or optimality criteria

• Local or global approximation

• Global convex approximation (for dynamics)

Integration in PERMAS

Compute power

• by fast solvers

• by parallelization

GUI support by PERMAS-FELIX

• for the specification of the design model

Results available via the usual interfaces

• Objective function history

• Element filling ratio

Bridge 2D Under Bridge and Train Weight

Beam 3D – Example of Prof. Fischer, FH Dortmund

6171 nodes

5000 elements and design variables

Run on Linux K7-500 with 100 MBmemory and 191 MB disk

16 iterations in 11m 51s elapsed

Support 3D – Example of Prof. Fischer, FH Dortmund

8022 nodes

6258 elements and 5226 designvariables

Run on K7-500 with 100 MB memoryand 235 MB disk

8 iterations in 9m 39s elapsed

Hook 3D – Example of Prof. Fischer, FH Dortmund

15204 nodes

12623 elements and design variables

Run on Linux K7-500 with 100 MBmemory and 435 MB disk

17 iterations in 59m 01s elapsed

Cantilever Beam – Eigenfrequency constraintsSource: Turner, M.J.: Design ofMinimum Mass Structures withSpecified Natural Frequencies,AIAA Journal, Vol. 5, March 1967,pp 406-412.

Material: Aluminiumti = 5.08E-03Ai = 6.45E-04mi = 1.363E+01Frequency constraint: f1 > 20 Hz

Cantilever Beam – Eigenfrequency constraints

Relative Effective Masses

------------------------------------------------------

Mode Frequency EffM_U [%] EffM_V [%] EffM_PHIW [%]

------------------------------------------------------

Sum 86.88 97.22 99.95

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1 1.98490E+01 0.87 64.56 94.49

2 8.78179E+01 2.30 21.81 4.16

3 1.84395E+02 54.78 1.79 0.87

4 2.30356E+02 9.86 8.95 0.28

5 3.71808E+02 19.06 0.12 0.15

Gas Pedal (iViP Study of Robert Bosch GmbH)

189503 elements

185525 nodes

556309 unknowns

Gas Pedal

Gas Pedal - Results

Stiffness objective achieved with 5% of the design space.

Analysis run on COMPAQ ES40:

•18 iterations

•3 GB memory

•10.2 GB disk

•24h 14m 28s elapsed sequential

•7h 53m 19s elapsed parallel

•Speed-up 3.1 on four processors

Summary

• Topology optimization integrated in PERMAS

• Fast solvers (supported by parallelization)

• Contact analysis available

• Statics and dynamic eigenvalues

• Very stable convergence behavior

INTES will develop this method further and willintegrate it with other types of optimization.