A multi-resolution parameterized level set method based on quasi-smooth manifold element

Abstract

This paper introduces a novel multi-resolution topology optimization method that combines the parametric level set method (PLSM) and quasi-smooth manifold element (QSME) [1]. The QSME has high accuracy and high-order continuity, and its degrees of freedoms have clear physical meanings. By employing the QSME for structural analysis on a coarser analysis mesh and PLSM for updating design variables on a finer design mesh, the proposed QSME-MPLSM can obtain clear and smooth optimized structures with high computational efficiency and reliable structural performance. By integrating the features of QSME and PLSM, this paper proposes an element subdivision technique (EST). The EST can accurately capture the integration domain of element and avoids the need for mesh refinement or additional element node. This paper presents a detailed formulation of the QSME-MPLSM for minimum compliance topology optimization problems, including sensitivity analysis, a design mesh generation method, and an EST-based element stiffness matrix update method. Representative 2D and 3D numerical examples are presented to validate effectiveness of the QSME-MPLSM. The results demonstrate that this method can enhance both the efficiency and accuracy of topology optimization, and obtain reliable optimized results.