Concurrent topology design of structure and material using a two-scale topology optimization

This paper presents new MIST (moving iso-surface threshold) formulation and algorithm for concurrent design of structural and cellular material topology. The material microstructure is assumed to be uniform in macro-scale, i.e. the macrostructure is composed of periodic unit cells. New formulations for the two physical response functions of macrostructure and microstructure (unit cell) are derived in terms of the results of finite element analyses of structure and material by using the homogenization theory. Several numerical examples are presented for optimum design solutions of the macrostructures and their corresponding material microstructures to illustrate the capability and efficiency of the present approach.