A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets

Abstract

This paper proposes a new multiscale topology optimization method for the concurrent design of multiphase composite structures under a certain range of excitation frequencies. Distinguished from the existed studies, a general concurrent design formulation for the dynamic composite structures with more than two material phases is developed. The macrostructureand its microstructures with multiple material phases are optimized simultaneously. The integral of the dynamic compliances over an interval of frequencies is formulated as the optimization objective, so as to minimize the frequency response within the concerned excitation range. The effective properties of the multiphase microstructures are evaluated by using the numerical homogenization method, which actually serves as a link to bridge the macro and micro finite element analyses. Furthermore, to describe the boundaries of multiple material phases for the microstructure, a parametric color level set method (PCLSM) is developed by using an efficient interpolation scheme. In this way, L level set functions can represent at most 2L material phases without any overlaps. Moreover, these “color” level sets are updated by directly using the well-established gradient-based algorithm, which can greatly facilitate the proposed method to solve the multi-material optimizations with multiple design constraints. Several 2D and 3D numerical examples are used to demonstrate the effectiveness of the proposed method in the concurrent design of the dynamic composite structures under the excitation frequency ranges.