A Concurrent Topology Optimization Model for Dynamic Property of Structures with Connectable Graded Microstructures

Abstract

Lattice structures composed of porous microstructures have attracted considerable attention due to their useful light-weight and multiphysical properties. Their mechanical properties are often a major concern in the design problem. However, unlike in the case of static stiffness maximization, few theoretical results can be used to guide the dynamic property design of such structures and their microstructures. In this paper, we present a numerical method of concurrent topology optimization for maximizing the natural frequencies of structures consisting of layer-wise graded microstructures. Both the configurations of graded microstructures and their spatial distribution in the macrostructural design domain are simultaneously optimized under constraints imposed on the macro- and microscales. The applied microscale design constraint still retains desired design space by allowing designable volume fractions of different microstructures under the total material usage restriction. The designable connective region technique is employed to guarantee the connectivity between different layers of microstructures. Numerical examples demonstrate the effectiveness of the proposed method. Compared to the uniform-lattice structural design, the proposed method is able to yield improved dynamic performance.