Scale‐related topology optimization of cellular materials and structures

TLDR

The paper discusses integrated optimization of lightweight cellular materials and structures, noting that conventional asymptotic homogenization predicts effective properties that depend only on volume fractions and ignore scale effects. The authors propose a design element (DE) concept that unifies conventional material and structural designs. They illustrate the DE concept by numerically designing 2D layered structures with cellular cores. Analysis shows that optimal solutions depend on scale‑effect modeling of the periodic microstructure (RVE), and varying the DE’s scale and aspect ratio reveals distinct scale‑related effects in the resulting optimal patterns. © 2006 John Wiley & Sons, Ltd.

Abstract

Abstract The integrated optimization of lightweight cellular materials and structures are discussed in this paper. By analysing the basic features of such a two‐scale problem, it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell (MUC), i.e. the so‐called representative volume element (RVE). However, with the asymptotic homogenization method used widely in actual topology optimization procedure, effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases, properties and spatial distribution of constituents in the microstructure regardless of scale effect. From this consideration, we propose the design element (DE) concept being able to deal with conventional designs of materials and structures in a unified way. By changing the scale and aspect ratio of the DE, scale‐related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns. To illustrate the proposed approach, numerical design problems of 2D layered structures with cellular core are investigated. Copyright © 2006 John Wiley & Sons, Ltd.