MULTIPHASE MATERIAL LAYOUT OPTIMIZATION CONSIDERING EMBEDDING MOVABLE HOLES

In structural engineering design, it is often necessary to embed one or more fixed-shaped holes to meet certain functional or manufacturing design requirements. To effectively solve the multi-phase material layout optimization problem of continuum structure with embedded movable holes, it is usually necessary to simultaneously optimize the position and orientation of these embedded holes and the topology configuration of the multi-phase material structure to improve the overall performance of the structure. To this end, parameterized level set functions are used to describe the geometry of the embedded holes. The material densities defining the structural topology of multiphase materials, and the geometric parameters used to describe the position and orientation of the embedded holes, are considered as design variables of the optimization problem considered here. To avoid the cumbersome of re-meshing the grids caused by the movement of holes and improve the efficiency of computation, the embedded holes are mapped into a density field on a fixed grid using a smoothed Heaviside function. Meanwhile, a SIMP-like material interpolation invoked at the finite element level is introduced for material parameterization of the optimization problem, and then the simultaneous optimization of the topology configuration of the multi-phase material structure and the position and orientation of the embedded hole can be realized. The material interpolation scheme supports full analytical sensitivity analysis, which allows the current optimization problem to be solved using gradient-based optimization algorithms. Numerical examples illustrate that the proposed method can effectively deal with the layout optimization problem of multiphase material embedded with multiple embedded holes.