A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE 2 Method

Ang Zhao, Vincent Beng Chye Tan, Pei Li, Kui Liu and Zhendong Hu ()
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Ang Zhao: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Vincent Beng Chye Tan: Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Pei Li: International Machinery Center, Department of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Kui Liu: Shanghai Aerospace Control Technology Institute, Shanghai 201109, China
Zhendong Hu: School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Mathematics, 2023, vol. 11, issue 12, 1-25

Abstract: The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE 2 method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE 2 model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.

Keywords: topology optimization; multiscale analysis; direct FE 2; reconstruction; filter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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