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<p>The iterative process of nonlinear analysis in topology optimization leads to high computational cost. To improve efficiency and convergence, a common strategy is to use a finer mesh for design and a coarser mesh for analysis. Coarse analysis meshes offer three key advantages: (1) faster convergence, (2) reduced computational time per iteration, and (3) lower risk of mesh distortion. However, the resolution mismatch can result in non-physical discontinuous material distributions within analysis elements, exhibiting characteristics of numerical artifacts of material discontinuities (i.e., QR-patterns). Multiresolution schemes, which decouple the design and analysis discretizations, can alleviate the above issues. To fully exploit the advantages of multiresolution schemes, we propose an <i>h</i>-refinement-based automated adaptive resolution method within the framework of isogeometric analysis. In this approach, an objective-based QR-patterns detection algorithm is activated during the convergence phase of the optimization. If QR-patterns are identified, the analysis mesh is automatically refined, thereby achieving an improved balance between accuracy and efficiency. Moreover, we propose a self-adjusting barrier regularization method that is particularly effective for large deformations and multiresolution meshes. This method automatically imposes penalties to resist mesh distortion, and further improving computational efficiency. Numerical results demonstrate that, compared to fixed-resolution strategies, the proposed adaptive framework achieves a superior trade-off between accuracy and cost. An additional contribution is a manufacturing-friendly post-processing strategy based on NURBS representation, enabling direct export of editable CAD models. Several numerical examples highlight the method’s advantages in terms of computational efficiency, geometric fidelity, and stability under large-deformation conditions.</p>

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Automated adaptive resolution framework with self-adjusting barrier regularization for stable nonlinear isogeometric topology optimization

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Xinqing Li,
  • Zhen-Pei Wang,
  • Yongzhen Mi,
  • David W. Rosen,
  • Yingjun Wang

摘要

The iterative process of nonlinear analysis in topology optimization leads to high computational cost. To improve efficiency and convergence, a common strategy is to use a finer mesh for design and a coarser mesh for analysis. Coarse analysis meshes offer three key advantages: (1) faster convergence, (2) reduced computational time per iteration, and (3) lower risk of mesh distortion. However, the resolution mismatch can result in non-physical discontinuous material distributions within analysis elements, exhibiting characteristics of numerical artifacts of material discontinuities (i.e., QR-patterns). Multiresolution schemes, which decouple the design and analysis discretizations, can alleviate the above issues. To fully exploit the advantages of multiresolution schemes, we propose an h-refinement-based automated adaptive resolution method within the framework of isogeometric analysis. In this approach, an objective-based QR-patterns detection algorithm is activated during the convergence phase of the optimization. If QR-patterns are identified, the analysis mesh is automatically refined, thereby achieving an improved balance between accuracy and efficiency. Moreover, we propose a self-adjusting barrier regularization method that is particularly effective for large deformations and multiresolution meshes. This method automatically imposes penalties to resist mesh distortion, and further improving computational efficiency. Numerical results demonstrate that, compared to fixed-resolution strategies, the proposed adaptive framework achieves a superior trade-off between accuracy and cost. An additional contribution is a manufacturing-friendly post-processing strategy based on NURBS representation, enabling direct export of editable CAD models. Several numerical examples highlight the method’s advantages in terms of computational efficiency, geometric fidelity, and stability under large-deformation conditions.