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<p>This study proposes an adaptive triangular mesh solid isotropic material with penalization (SIMP) method for topology optimization, enhancing geometric adaptability beyond the constraints of quadrilateral meshes. By introducing a modified filtering operator with an area ratio multiplier, the method effectively mitigates numerical instabilities that arise from mesh dependency while adaptively refining grayscale elements. Results validate its robustness across truss, cantilever, and multi-load cases, offering a practical framework for complex structural optimization. The numerical results demonstrate that our method achieves structures with sharper boundaries and increases stiffness relative to those obtained using quadrilateral mesh approaches. Compared with using a uniform triangular mesh, this approach achieves similar optimal designs with fewer than half the elements of a uniform triangular mesh, while reducing approximately 10 % lower compliance and near-zero gray area. In particular, its ability to create perfect 0–1 structures in certain cases highlights the method’s robustness and practical manufacturability.</p>

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Adaptive triangular mesh SIMP method with modified filtering

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Nian Zhang,
  • You Zhang,
  • Zhanbin Yuan

摘要

This study proposes an adaptive triangular mesh solid isotropic material with penalization (SIMP) method for topology optimization, enhancing geometric adaptability beyond the constraints of quadrilateral meshes. By introducing a modified filtering operator with an area ratio multiplier, the method effectively mitigates numerical instabilities that arise from mesh dependency while adaptively refining grayscale elements. Results validate its robustness across truss, cantilever, and multi-load cases, offering a practical framework for complex structural optimization. The numerical results demonstrate that our method achieves structures with sharper boundaries and increases stiffness relative to those obtained using quadrilateral mesh approaches. Compared with using a uniform triangular mesh, this approach achieves similar optimal designs with fewer than half the elements of a uniform triangular mesh, while reducing approximately 10 % lower compliance and near-zero gray area. In particular, its ability to create perfect 0–1 structures in certain cases highlights the method’s robustness and practical manufacturability.