Integrated Design of Micro Configuration and Macro Arrangement with Scale-Coupled Effect for Maximum the Fundamental Frequency

Abstract

It is well known that structural behaviors of composite solids are determined by topology of microstructures of different sizes. In this paper a concurrent topology optimization method for integrated design of materials and structures with periodical microstructure was presented. The microstructures were assumed to be uniform in macro scale and heterogeneous in micro scale and the optimization object was to maximize the material fundamental frequency. Design variables for structure and material microstructures were defined, independently. RAMP (Rational Approximation ofMaterial Properties) was adopted to ensure clear topologies in both macro and micro scales. Design variables for structure and material microstructures were integrated into one system by using the super-element method. Influences of Representative Volume Element sizes, the microstructure configuration and macro arrangement are investigated. Numerical experiments validate the proposed method which can be used as an innovative design concept for the lightweight structures.