A bionic topology optimization method with an additional displacement constraint

Yuhai Zhong; Huashan Feng; Hongbo Wang; Runxiao Wang; Weiwei Yu; Yuhai Zhong; Huashan Feng; Hongbo Wang; Runxiao Wang; Weiwei Yu

doi:10.3934/era.2023037

Electronic Research Archive

2023, Volume 31, Issue 2: 754-769. doi: 10.3934/era.2023037

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A bionic topology optimization method with an additional displacement constraint

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Received: 27 September 2022 Revised: 08 November 2022 Accepted: 12 November 2022 Published: 22 November 2022

Displacement is an important measure of stiffness, and its constraint must be considered in many real engineering designs. However, traditional volume-constrained compliance minimization methods for load-bearing structures do not deal with displacements of practical importance directly. Based on this situation, the paper extends an improved bionic topology optimization method to solve the topology optimization problem with an additional displacement constraint. The updates of density design variables are based on an improved bone remodeling algorithm rather than gradient information employed by traditional methods. An explicit relationship between the threshold in the bone remodeling algorithm and target node displacement is constructed to satisfy displacement constraint. As a result, one will obtain a topology with an optimal cost-weighted sum of stiffness and mass while the target node displacement does not exceed its predefined limit. 2D and 3D examples are given to demonstrate the effectiveness of the proposed method.
- topology optimization,
- engineering optimization,
- displacement constraint,
- bone remodeling algorithm
Citation: Yuhai Zhong, Huashan Feng, Hongbo Wang, Runxiao Wang, Weiwei Yu. A bionic topology optimization method with an additional displacement constraint[J]. Electronic Research Archive, 2023, 31(2): 754-769. doi: 10.3934/era.2023037

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Abstract

Displacement is an important measure of stiffness, and its constraint must be considered in many real engineering designs. However, traditional volume-constrained compliance minimization methods for load-bearing structures do not deal with displacements of practical importance directly. Based on this situation, the paper extends an improved bionic topology optimization method to solve the topology optimization problem with an additional displacement constraint. The updates of density design variables are based on an improved bone remodeling algorithm rather than gradient information employed by traditional methods. An explicit relationship between the threshold in the bone remodeling algorithm and target node displacement is constructed to satisfy displacement constraint. As a result, one will obtain a topology with an optimal cost-weighted sum of stiffness and mass while the target node displacement does not exceed its predefined limit. 2D and 3D examples are given to demonstrate the effectiveness of the proposed method.

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