Multiscale topology optimization for minimizing frequency responses of cellular composites with connectable graded microstructures

摘要

This paper develops an efficient multiscale topology optimization method for minimizing the frequency response of cellular composites over a given frequency interval, which consist of spatially-varying connectable graded microstructures. In this method, multiple prototype microstructures are topologically optimized in a progressive manner considering the sensitivity information of two adjacent prototype microstructures, achieving their similar topological configurations. A shape interpolation method is employed to interpolate the shapes of the prototype microstructures to generate a series of graded microstructures from the solid one to void, which are featured with essential interconnections generated by similar shapes of these prototype microstructures. The variable thickness sheet method is adopted at macroscale to generate a free material distribution under a global volume constraint. In order to reduce the computational burden, at microscale, a Kriging metamodel constructed by key graded microstructures as sample points is employed to predict the effective properties of all the microstructures within macrostructure. Furthermore, at macroscale, the quasi-static Ritz vector method is incorporated for efficient frequency response analysis. The method of moving asymptotes is adopted to update the design variables at both scales. In the proposed method, the configurations of spatially-varying connectable graded microstructures at microscale and their distribution at macroscale are simultaneously optimized, which ensures a sufficiently large design space to minimize the frequency response of cellular composites. The topological variations of multiple prototype microstructures further expand this advantage. Numerical examples are provided to test the performance of the proposed multiscale topology optimization method for minimizing the frequency responses of cellular composites.