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<p>This study presents a novel method for solving stress-constrained topology optimization (TO) problems by combining the polygonal finite element method with the renormalization-free maximum-rectifier-function (MRF) approach. Unlike conventional aggregation techniques that require stress constraint renormalization and exhibit high sensitivity to aggregation parameters, the proposed MRF-based framework ensures robust convergence and clear topological definition. The MRF method employs a differentiable rectifier function and a lower-bound form of the Kreisselmeier-Steinhauser function to effectively aggregate local stress constraints, ensuring compliance with the allowable stress limit without inducing stress concentrations. To enhance numerical stability and contrast between solid and void regions, a threshold projection scheme is incorporated alongside a linear density filter and modified SIMP model. Furthermore, the use of polygonal elements offers increased flexibility in meshing complex geometries, enabling smooth topology transitions during optimization. The effectiveness of the proposed approach is demonstrated through two benchmark problems—including the L-bracket, Hook-shaped, and portal frame structures—showcasing its advantages in stress distribution control, mesh independence, and computational efficiency.</p>

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Renormalization-free of maximum stress aggregation in stress-constrained topology optimization with polygonal spatial discretization

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Son H. Nguyen,
  • Duc-Huynh Phan

摘要

This study presents a novel method for solving stress-constrained topology optimization (TO) problems by combining the polygonal finite element method with the renormalization-free maximum-rectifier-function (MRF) approach. Unlike conventional aggregation techniques that require stress constraint renormalization and exhibit high sensitivity to aggregation parameters, the proposed MRF-based framework ensures robust convergence and clear topological definition. The MRF method employs a differentiable rectifier function and a lower-bound form of the Kreisselmeier-Steinhauser function to effectively aggregate local stress constraints, ensuring compliance with the allowable stress limit without inducing stress concentrations. To enhance numerical stability and contrast between solid and void regions, a threshold projection scheme is incorporated alongside a linear density filter and modified SIMP model. Furthermore, the use of polygonal elements offers increased flexibility in meshing complex geometries, enabling smooth topology transitions during optimization. The effectiveness of the proposed approach is demonstrated through two benchmark problems—including the L-bracket, Hook-shaped, and portal frame structures—showcasing its advantages in stress distribution control, mesh independence, and computational efficiency.