An efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR) is proposed to construct mapping between the mesh before modification and after modification during the optimization process. Subsequently, MG‐IGR is utilized to reanalyze the modified design efficiently by reusing the initial evaluated results. Moreover, the proposed MG‐IGR also eliminates the restriction of mesh consistency. In this framework, the structure can be designed directly through parameterized control of the non‐uniform rational B‐spline (NURBS) model, and the MG‐IGR fast solver enables any metaheuristic algorithm to perform the optimization procedure. Moreover, the accuracy of the simulation can be guaranteed by the NURBS model and the convergence criterion of the MG. Finally, two geometric optimization examples are presented to validate the performance of the developed framework.

中文翻译：

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一种基于辅助投影的高效多网格等几何再分析方法及其在优化框架中的应用

通过整合基于辅助投影的多网格等几何重分析（MG-IGR）和元启发式搜索技术，本研究开发了一种有效的优化框架。众所周知，等角几何分析（IGA）的固有特性在形状优化问题上具有优势。继承了IGA的特性，提出了一种基于投影的辅助MG重新分析（MGR），以在优化过程中构造修改之前和修改之后的网格之间的映射。随后，通过重新使用初始评估结果，利用MG-IGR有效地重新分析修改后的设计。此外，提出的MG-IGR还消除了网格一致性的限制。在这个框架中 可以通过非均匀有理B样条（NURBS）模型的参数控制直接设计结构，并且MG-IGR快速求解器使任何元启发式算法都能执行优化程序。此外，可以通过NURBS模型和MG的收敛准则来保证仿真的准确性。最后，给出了两个几何优化示例，以验证所开发框架的性能。