Combined Topology and Shape Optimization of Structures using Nodal Density as Design Parameter

Abstract

In this study, a new nodal–based distribution method of material properties is proposed for material topology optimization in linear elastostatic structures. It is based on a design domain concept of a density distribution method (Bendsøe, 1989). Nodal densities of material properties are considered as optimization design variables. Geometric boundaries are represented by fixed grids, thus an Eulerian type of formulation is used for optimal interfaces. The objective is to obtain both optimal smooth shapes and topologies based on the design domain concept avoiding an excessive number of finite elements. This approach allows us to perform a nodal–based topology and shape optimization, which can be easily implemented in existing gradient–based optimization codes. Numerical examples demonstrate the efficiency of the present method.