Concurrent topology optimization for structures and celluar materials based on Kriging model

Abstract

Hierarchical structures exhibit superior properties, such as light weight, energy absorption, vibration isolation, thermal insulation and permeability, etc. This paper aims to enhance the multiscale topology optimization efficiency based on the Kriging model, a smooth evolutionary method is employed to evolve and form the structural topologies. Specifically, the proposed method optimizes the microstructural dimensions and macrostructural topologies at the same time, which can greatly reduce the computation time. First of all, a microstructural library is constructed, from which the microstructures best satisfy the macroscopic boundary conditions of the experiments are selected. Then, a parameterized design of the microstructures based on the Kriging model is conducted. Subsequently, the macroscopic structure is obtained by topology optimization and periodically arranged by the optimal microstructure. The macroscopic equivalent properties of the microstructures are evaluated by the homogenization method. Finally, the effectiveness, accuracy and efficiency of the proposed method for the design of hierarchical structures, are illustrated by comparing the results with those obtained by the sample method.