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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.

An efficient multi-resolution topology optimization scheme for stiffness maximization and stress minimization