Concurrent topology optimization of composite macrostructure and microstructure constructed by constituent phases of distinct Poisson's ratios for maximum frequency

Abstract

This paper introduces a two-scale concurrent topology optimization method for maximizing the frequency of composite macrostructure that are composed of periodic composite units (PCUs) consisting of two isotropic materials with distinct Poisson’s ratios. Interpolation of Poisson’s ratios of different constituent phases is used in PCU to exploit the Poisson effect. The effective properties of the composite are computed by numerical homogenization and integrated into the frequency analysis. The sensitivities of the eigenvalue of macro- and micro-scale density are derived. The design variables on both the macro- and micro-scales are efficiently updated by the well-established optimality criteria methods. Several 2D and 3D illustrative examples are presented to demonstrate the capability and effectiveness of the proposed approach. The effect of the micro-scale volume fraction and Poisson’s ratio of the constituent phases on the optimal topology are investigated. It is observed that higher frequency can be achieved at specific range of micro-scale level volume fraction for optimal composites than that obtained from structures made of individual base materials.