This article develops a multi-resolution topology optimization (MTOP) approach based on the solid isotropic material with penalization (SIMP) method, which is effective in obtaining high-resolution designs at low computational cost. The extended finite element method (XFEM) is employed to decouple the analysis mesh, material description and nodal design variables. By the advantage of XFEM at modelling material discontinuity, detailed geometrical features are generated on a coarse analysis mesh. To obtain a clear interface between material grids, a variation of the traditional sensitivity filter is introduced to produce discrete solutions. The low computational costs make the proposed approach appropriate for dealing with problems requiring a high number of finite element analysis (FEA) processes, typically high-resolution/large-scale models, stress minimization, etc. Accurate von Mises stress is calculated on a high number of Gaussian points, making the approach perform better at stress minimization. Then, several 2D and 3D examples optimized by different solvers are illustrated to demonstrate the effectiveness and excellent generality of the proposed approach.

本文开发了一种基于固体各向同性材料的惩罚化（SIMP）方法的多分辨率拓扑优化（MTOP）方法，该方法可有效地以较低的计算成本获得高分辨率的设计。扩展有限元方法（XFEM）用于分离分析网格，材料描述和节点设计变量。利用XFEM建模材料不连续性的优势，可以在粗糙的分析网格上生成详细的几何特征。为了在材料网格之间获得清晰的界面，引入了传统灵敏度滤波器的一种变体以产生离散的解决方案。较低的计算成本使所提出的方法适合于处理需要大量有限元分析（FEA）过程（通常是高分辨率/大规模模型）的问题，等精确von Mises应力计算在高数目的高斯点，使得在方法最小化应力更好执行。然后，说明了由不同求解器优化的几个2D和3D示例，以证明所提出方法的有效性和出色的通用性。