Toplogical optimization of structures using Fourier representations

White, Daniel A.; Stowell, Mark L.; Tortorelli, Daniel A.

doi:10.1007/s00158-018-1962-y

Toplogical optimization of structures using Fourier representations

Journal Article · Mon Apr 02 00:00:00 EDT 2018 · Structural and Multidisciplinary Optimization

DOI:https://doi.org/10.1007/s00158-018-1962-y· OSTI ID:1479078

White, Daniel A. ^[1]; Stowell, Mark L. ^[1]; Tortorelli, Daniel A. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

The minimization of compliance subject to a mass constraint is the topology optimization design problem of interest. The goal is to determine the optimal configuration of material within an allowed volume. Our approach builds upon the well-known density method in which the decision variable is the material density in every cell in a mesh. In it’s most basic form the density method consists of three steps: 1) the problem is convexified by replacing the integer material indicator function with a volume fraction, 2) the problem is regularized by filtering the volume fraction field to impose a minimum length scale; 3) the filtered volume fraction is penalized to steer the material distribution toward binary designs. The filtering step is used to yield a mesh-independent solution and to eliminate checkerboard instabilities. In image processing terms this is a low-pass filter, and a consequence is that the decision variables are not independent and a change of basis could significantly reduce the dimension of the nonlinear programming problem. Based on this observation, we represent the volume fraction field with a truncated Fourier representation. Furthermore, this imposes a minimal length scale on the problem, eliminates checkerboard instabilities, and also reduces the number of decision variables by over 100 × (two dimensions) or 1000 × (three dimensions).

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1479078

Report Number(s):: LLNL-JRNL--736779; 889675

Journal Information:: Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 3 Vol. 58; ISSN 1615-147X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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