Abstract
Topological constraints have recently been introduced to structural topology optimization by the BESO method. However, for the classical and widely used SIMP-type optimization method, an implicit and continuously changing variable cannot express the topological characteristics directly during the optimization process. This is partly caused by missing well-defined boundaries to compute topological characteristics. To introduce topological constraints into the SIMP-type method, an auxiliary discrete expression of structural boundaries through the volume preservation projection method is used to compute topological characteristics, that is, the genus or number of holes. A topological control methodology based on persistence homology, a numerical calculation idea derived from topological data analysis, is introduced in this paper to implement topological constraints. With the help of the design space progressive restriction method, the proposed methodology shows that for the 2D static minimum compliance optimization problem, the inequality constraints on the number of holes can be satisfied. The effectiveness of the proposed topological control method for the SIMP-type framework is illustrated by several numerical examples.
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This research was funded by the National Natural Science Foundation of China (No. 51675506) and the National Key Research and Development Program of China (No. 2018YFF01011503).
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We consider that the key algorithm for controlling the number of holes is well explained by the persuasion algorithm chart and can be easily repeated. The strategy of the DSPRM is defined in Sect. Design Space Progressive Restriction Method (DSPRM) and the formulae are listed. For the code of the FBM method, one can refer to topological control work based on the BESO method (Han et al., 2021). The pre-generated filter matrix codes are modified based on Andreassen’s 88-line MATLAB work (Andreassen et al., 2010).
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Wang, Q., Han, H., Wang, C. et al. Topological control for 2D minimum compliance topology optimization using SIMP method. Struct Multidisc Optim 65, 38 (2022). https://doi.org/10.1007/s00158-021-03124-6
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DOI: https://doi.org/10.1007/s00158-021-03124-6