A Displacement-Based Topology Design Method with Self-Adaptive Layered Materials

Abstract

The earliest literature on topology optimization involves layout problems. For example, Prager, Rozvany and others have studied layout optimization of truss structures, a problem which results in optimal designs with many thin, `truss-like' members [1], [2]. The first attempts to optimize continua over variable topologies were based on macroscopic partitions of the candidate structure domain into solid and void regions [3]. However, it was found that this formulation of the topology optimization problem is not well-posed [4]. Kohn and Strang obtained a well-posed, relaxed formulation by quasiconvexification and, alternatively, by homogenization of a microstructural model [4]. The relaxed problem can be approximated using a finite element grid on a fixed domain [5]. Bendsoe and Kikuchi explored this approach using a microstructure that approximates the optimal configuration [6].