Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency

Ultra-light cellular materials exhibit high stiffness/strength to weight ratios and bring opportunity for multifunctional performance. One of their potential applications is to build structure with optimum dynamic performance, which is extremely important for some structural parts in vehicle engineering and attracts a great attention. This paper presents a two-scale optimization method and aims at finding optimal configurations of macro structures and micro-structures of cellular material with maximum structural fundamental frequency. In this method macro and micro densities are introduced as independent design variables for macrostructure and microstructure. Optimizations at two scales are integrated into one system through homogenization theory and base material is distributed between the two scales automatically with optimization model. Microstructure of materials is assumed to be homogeneous at the macro scale to meet today's manufacture practice and reduce manufacturing cost. Plane structure with homogeneous cellular material and perforated plate are studied. Numerical experiments validate the proposed method and computational model.