Gradient-based concurrent topology and anisotropy optimization for mechanical structures

Abstract

The present paper introduces a novel gradient-based optimization framework to obtain discrete topologies consisting of either none or complete presence of anisotropic material, modeled by means of the polar formalism. Current topology optimizations with the polar formalism are based on optimality criteria, and limited to performing compliance minimization for thermodynamically feasible materials. The proposed optimization approach uses a sequential approximations approach, based on the Methods of Moving Asymptotes. The material density, orientation and anisotropic modules are updated separately at each iteration, in parallel sub-problems constructed with different types of approximations and settings. The proposed optimization approach is successfully validated for compliance minimization against the Alternate Directions method for general orthotropic materials, defined by the thermodynamic bounds. The importance of the anisotropy initialization in the gradient-based approach is highlighted to obtain stiffer solutions. The gradient-based strategy is also extended to incorporate geometric bounds on the polar parameters, defining the domain of existence of composite laminates. Obtained results for compliance minimization with laminates are compared to published results using lamination parameters. Finally, new solutions are presented showing the improvement of the compliance with the expansion of the anisotropy design domains. This paper paves the way for strength-based topology optimization of parts made of orthotropic materials or composite laminates.