Multi-scale concurrent topology optimization of lattice structures with single type of composite micro-structure subjected to design-dependent self-weight loads

Abstract

This paper presents a computational framework for compliance-based multi-scale concurrent topology optimization including self-weight. The macro-scale structure consists of periodically arranged composite micro-structures, such that the representative unit cell of each micro-structure is composed of multiple base-materials, instead of single base-material as usually encountered in the literature. The effective elastic tensor of the micro-structure is evaluated using the strain energy method (SEM), which is incorporated with a mapping based interpolation scheme for multiple underlying materials. Sensitivity analysis is executed in both macro-scale and micro-scale, providing the gradient information for updating the design variables using the method of moving asymptotes (MMA). The undesirable phenomena related to the design-dependent self-weight load are observed, including the parasitic effect and the inactive volume constraint. When the self-weight load is dominant over the external fixed loads, especially in the case of pure self-weight, the optimizer tends to remove material to reduce self-weight, and thus reduces the structural compliance. This phenomenon, which is referred as inactive volume constraint in the literature, occurs at both scales. On the other hand, the parasitic effect, which is the appearance of erratic intermediate density patterns, occurs only in the macro-structure but not in the micro-structure. Discussion on possible treatments for these numerical issues is provided. Several numerical examples of 2D structures are examined to demonstrate the feasibility and performance of the developed method.