Evolutionary Structural Topology Optimization for Continuum Structures with Structural Size and Topology Variables

Abstract

In this paper, a topology optimization method mixed structures with continuum and discrete elements is proposed. First, based on the stress and displacement formulations of the finite element analysis, a set of stress sensitivity numbers for beam and plane-stress structures are derived. Then, relative difference quotients for topology and size variables of mixed continuum structures with several different types of components are formulated. The optimization criteria, which incorporate the element stress level and relative different quotients, are developed for the topology optimization of continuum domains and the sizing optimization of discrete elements. A new optimization procedure based on the bi-directional evolutionary structural optimization method is proposed. Two examples are provided to demonstrate the validity and effectiveness of the proposed method.