Topology optimization of arbitrary-shape multi-phase structure with structured meshes based on a virtual phase method

Abstract In the community of topology optimization , the contradiction between the frontier research with structured meshes and the complex geometry in the real-world problems has existed for a long time. Structured mesh is attractive in convenient application of loads and boundary conditions, and easy implementation of GPU parallel calculation. Therefore, unlike existing researches solving the issue through unstructured elements, this paper presents an easy-to-accomplish virtual phase method (VPM) based on structured meshes, to systematically solve the problems with complex geometries and arbitrary non-design domains. Structural geometry is denoted by the extended regular design domain and void region initially placed at the border of the extended domain. Based on the extended idea of composite material interpolation in multi-phase density-based topology optimization approaches, the extended structural design domains and the pre-defined non-design domains are considered as the optimized phases in the structure, and they are defined by discrete variable fields. Subsequently, the structural optimization is implemented like as the traditional multi-material topology optimization process. Numerical examples accounting for minimum compliance are presented to demonstrate the effectiveness of the proposed method, including multi-phase macrostructural design, the ease with which the method can accommodate passive regions, and how the length scale constraints are used to devise graded porous infill morphology within a given shell. At last, the manufacturability of the optimized designs is discussed to further verify the applicability of the proposed method. Our approach provides those front researches based on structured meshes with an easily accessible access, to be straightforwardly applied for any complex-domain design problem.