Because finite elements and density elements are separated in multi-resolution topology optimization (MTOP), a relatively fewer number of finite elements can be used, thereby significantly reducing computing cost in finite element analysis (FEA) during topology optimization. However, for large-scale problems, numerous design variables are still required to precisely represent the optimum topology. This causes a dominant computational burden in design optimization. In this paper, an efficient multi-resolution topology optimization (MTOP) using adaptive isosurface variable grouping (aIVG) is proposed to alleviate the above computational burden in topology optimization by grouping design variables of similar grouping criteria into a single grouped design variable. Adaptive isosurface variable grouping is performed according to the grouping criterion which can be calculated using design variables and their sensitivities. Numerical examples such as 2D and 3D compliance minimization, 2D compliant mechanism, 2D multiple displacement constraints, and 3D thermal compliance minimization demonstrate that the proposed MTOP-aIVG significantly reduces computation time in optimization by virtue of using a reduced number of design variables.

由于在多分辨率拓扑优化（MTOP）中将有限元和密度元分开，因此可以使用相对较少数量的有限元，从而显着降低了拓扑优化过程中有限元分析（FEA）中的计算成本。但是，对于大规模问题，仍然需要大量设计变量来精确表示最佳拓扑。这导致了设计优化中的主要计算负担。本文提出了一种利用自适应等值面变量分组（aIVG）的高效多分辨率拓扑优化（MTOP），通过将相似分组标准的设计变量分组为单个分组的设计变量来减轻拓扑优化中的上述计算负担。根据可以使用设计变量及其敏感度计算出的分组标准执行自适应等值面变量分组。诸如2D和3D依从性最小化，2D依从性机制，2D多位移约束和3D热依从性最小化的数值示例表明，所提出的MTOP-aIVG通过使用数量减少的设计变量而大大减少了优化中的计算时间。