Stress-constrained concurrent multiscale topological design of porous composites based on discrete material optimisation

TY - JOUR

T1 - Stress-constrained concurrent multiscale topological design of porous composites based on discrete material optimisation

AU - Wei, Guangkai

AU - Chen, Yuan

AU - Han, Xu

AU - Li, Guixing

AU - Bai, Yingchun

AU - Fu, Kunkun

N1 - Publisher Copyright: © 2024 Elsevier Inc.

PY - 2025/1

Y1 - 2025/1

N2 - Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.

AB - Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.

KW - Discrete material optimisation

KW - Isogeometric analysis

KW - Multiscale topology optimisation

KW - Porous composites

KW - Stress constraint

UR - https://www.scopus.com/pages/publications/85205147616

U2 - 10.1016/j.apm.2024.115730

DO - 10.1016/j.apm.2024.115730

M3 - Article

AN - SCOPUS:85205147616

SN - 0307-904X

VL - 137

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

M1 - 115730

ER -