Multimaterial multijoint topology optimization

Abstract

Summary In this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.

Simultaneous single‐loop multimaterial and multijoint topology optimization

“…The rules for good joint design set out first by Woischwill and Kim and also used by Florea et al will be adopted as the criteria for correct joint design: “All components of dissimilar materials must either be connected through joints or disconnected altogether (i.e. separated by void elements), such that no load can pass directly through dissimilar material interfaces.” “Joints can only exist along dissimilar material interfaces; it is assumed that all components of a single material can be formed without the need for joining.” …”

“…This is the joint cost interpolation function. As shown in both References and , only the cost of joint elements is considered in this work; thus, cost values will only exist for elements where is 1 and have been identified as interface elements. Furthermore, while cost values will be given in units of [$], this is done only to make results easier to interpret.…”

“…In order to perform MM & MJ TO, a method must first be developed for reliably determining which elements lie on the dissimilar material interface. Based on the joint design rules set out by Woischwill and Kim, dissimilar materials cannot have direct load transfer (“perfectly fused”). They must either be completely disconnected (void) or connected through a joint material.…”

“…The choice of joint type often requires a change in the shape of the base components. While Woischwill and Kim and Florea et al did consider the aspect of designing with multiple materials and multiple joints in the algorithm, the true coupling between MMTO and MJTO has yet to be explored. Thus, the current knowledge gap in the field of MMTO is simultaneously determining not only optimal MM design but also optimal MJ design between the components.…”

“…The objective of this article is to expand on the work previously introduced by Woischwill and Kim and Florea et al through the improvement of core theory, based on a new SIMP‐like density‐based interpolation scheme, addressing limitations of these studies. First, the proposed method will not require two separate TO runs, but the entire process will be self‐contained in a single loop—whereas Woischwill and Kim and Florea et al used a double‐loop approach. Ultimately, this means that the proposed method will perform optimization more effectively by accurately considering the coupling between MMTO and MJTO.…”