Multiscale topology optimisation for porous composite structures with stress-constraint and clustered microstructures

Abstract

While porous composites are drawing growing attention for their excellent lightweight and multifunctional characteristics, inherent stress concentration in these porous composites often presents a main concern of structural integrity. This study aims to develop a multiscale topology optimisation (MTO) method for design of porous composites with clustered microstructures under a prescribed stress constraint. First, the concurrent topology optimisation (TO) for both macrostructures and microstructures are implemented via a multiscale algorithm. Meanwhile, a clustering technique is implemented based on a so-called k-means method to simultaneously determine the allowable volume fraction and microstructural configuration. Second, a consistent density-and-strain based clustering technique is developed for both 2D and 3D multiscale TO. Finally, two benchmark design examples, namely Messerschmitt–Bölkow–Blohm (MBB) and L-bracket structures, are implemented using the presented MTO method by considering either 2D or 3D situations to demonstrate the design effectiveness. The results indicate that, when optimising a high-stiffness porous composites subject to the stress constraint, the maximum von Mises stresses of the 2D MBB and L-bracket structures are well restrained, which are respectively 20% and 29% lower than those without the stress-constraint. In design of a 3D L-bracket, the present MTO method can achieve around 19% reduction in the maximum stress. The study demonstrates the importance of stress constraint to the topological design of multiscale porous composite structures.