Hierarchical topology optimization addressing material design constraints and application to sandwich-type structures

The hierarchical topology optimization model for multiscale design of structures addresses the problem of finding optimal material distributions at different but interconnected structural length scales with the objective of optimally design the structure and its material. In this work some new developments on this model are presented. An algorithm is mounted to address specific features of multiscale design such as multiple material design constrains. Furthermore, previous design parameterizations assume micro design variables associated with each finite element, trying to approximate a pointwise optimal material definition, and leading to very efficient designs but of problematic manufacturability. Here one reduces the total number of problem design variables by assuming a design parameterization where the design is uniform within mechanically consistent larger subdomains—“design subdomains”. This eases applicability, manufacturability, and is a very effective approach for practical design problems involving for example sandwich-type structures, where larger subdomains identify structural constituents such as a soft core between two solid face-sheets. The parameterization to include “design subdomains” and the introduction of local material design constraints requires an appropriate derivation of the optimality conditions. The main structural applications presented here are related to sandwich type of structures. The influence of the designer choices for “design subdomains” characterizing the macrostructure, and “material unit cell” representing the microstructure, will also be studied in the solutions obtained. The examples show the effectiveness of the methodology presented to fully benefit from an enlarged design space incorporating structural and material designs, and thus efficiently maximize the mechanical component structural performance.