Toplogical optimization of structures using Fourier representations
- 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).
- Research Organization:
- Lawrence Livermore National Lab. (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, Vol. 58, Issue 3; ISSN 1615-147X
- Publisher:
- SpringerCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
A dual mesh method with adaptivity for stress-constrained topology optimization
|
journal | November 2019 |
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