On design-set restriction in SAND topology optimization
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We study design-set restriction—i.e., the issue of nonexistence of solutions, mesh-dependence, and local minima—in the alternative SAND (‘simultaneous analysis and design’, or ‘direct’) setting of the classical SIMP minimum compliance topology optimization problem. Compared to some predominant filtering techniques, which are typically studied in the conventional NAND setting, so-called ‘slope constraints’—point-wise bounds on the gradient of the material distribution function—necessitate only a reasonable amount of computational resources in the alternative SAND setting. The numerical method is based on a standard finite element procedure and sequential approximate optimization (SAO) method. Numerical experiments with a random multistart strategy and a simple relaxation procedure suggest that ‘probably’ globally optimal 0-1 designs may be obtained in a reasonable amount of computation time.
KeywordsTopology design Simultaneous analysis and design (SAND) Quasi-Newton methods Finite element methods Restriction methods Slope constraints
The authors wish to thank Stellenbosch University’s Department of Mechanical and Mechatronic Engineering for financial support, and Charl Möller, administrator of the Rhasatsha HPC, for technical assistance and support. Gratitude is also extended to the reviewers of the manuscript, whose willingness to comment, criticize, and suggest improvement, contributed to a manuscript of increased quality.
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