Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity

ZHANG Manzhe; GU Shuitao; FENG Zhiqiang

doi:10.21656/1000-0887.450038

Volume 46 Issue 1

Jan. 2025

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ZHANG Manzhe, GU Shuitao, FENG Zhiqiang. Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity[J]. Applied Mathematics and Mechanics, 2025, 46(1): 12-28. doi: 10.21656/1000-0887.450038

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Bidirectional Evolutionary Topology Optimization for Stress Minimization Based on the Modified Couple Stress Elasticity

doi: 10.21656/1000-0887.450038

1. School of Civil Engineering， Chongqing University， Chongqing 400040， P.R.China;
2. School of Mechanics and Engineering， Southwest Jiaotong University，Chengdu 610031， P.R.China

Received Date: 2024-02-22
Rev Recd Date: 2024-03-17

Abstract

Abstract

The application of stress-based bidirectional evolutionary structural optimization (BESO) in the context of the modified couple stress elasticity theory was investigated. This methodology allows for structure optimization of homogenized continuum with a microstructural composition of size effects. The classical BESO technique was extended through the introduction of a novel formulation of couple stress based non-classical equivalent stress, and the minimization design was conducted under the constraint of volume criterion. The iterative update of design variables relies on the sensitivity analysis involving direct derivation of the enriched p-norm global stress with couple stress contributions. Since the high-order elasticity is involved, the FEM implementation requires at least the C¹ nodal continuity. Thus, a Lagrangian finite element complemented by additional integration functions was implemented. The method was validated with 3 distinct cases through investigation of the size effects on the stress optimization and the subsequent structure design. The impacts of other parameters including the norm p value and the material volume fraction, were explored. The results demonstrate the potential of the proposed stress-based BESO method in addressing structural optimization of problems involving size effects.
- topology optimization,
- BESO,
- stress-based,
- modified couple stress,
- size effect

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References(42)

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