抄録
Structural optimization has been used not only for structural design but also, recently, for material microstructural design. Microstructural optimization methods are categorized into two types: one aims to control material properties while the other aims to improve the performance of a structure. Most microstructural optimization methods are based on the homogenization method which assumes that the microstructures are infinitesimally small, but these microstructures actually have a fmite size. On the other hand, micropolar continuum theory enables us to handle materials whose microstructures are finite in size as homogeneous materials. This theory introduces rotational degrees of freedom in addition to the usual translational degrees of freedom and requires new material constants, such as characteristic length. Micropolar constants are derived in cases where the microstructure has a lattice pattern, although they are generally unknown. We therefore propose a method for optimizing the lattice widths of a microstructure at each point by approximating the material as a micropolar elastic solid so that the performance of a structure can be improved. The proposed method is applied to several numerical examples in order to demonstrate its effectiveness.
