A Mesh Independent Approach for Multi-Joint Topology Optimization

Abstract

Topology optimization (TO) has been identified as a leading method to reduce weight in both component and assembly level design. Optimum loadpaths within a designable region are determined, providing non-intuitive designs that can result in significant weight savings while adhering to structural performance criteria. Multi-material topology optimization (MMTO) is a subset of TO, which extends the problem to consider material selection and material existence simultaneously. Multi-material solutions, therefore, represent an assembly where each section of dissimilar material is a different component. Conventional MMTO, however, assumes perfect joining between dissimilar materials, omitting joining. Therefore, a manual solution interpretation process is required to add joints to these solutions. Once joints are added, performance metrics (i.e. compliance and mass) are subject to change. Multi-joint topology optimization (MJTO) directly addresses this issue, adding joining within the optimization problem. Interfaces between dissimilar materials are modeled as joints, which can impact the substrate loadpath and material selection. Previously presented MJTO methodologies are restricted to uniform meshes, limiting the scope of problems which the method can be applied. In this work, a novel interface detection methodology is presented, expanding the MJTO methodology to irregular, non-uniform mesh types. A revision to the previously presented analytical sensitivities is presented to consider the coupling between adjacent elements resulting from the convolution operation in the interface detection procedure. The revised MJTO methodology is demonstrated with a series of case studies employing both academic and industry level models. A comparison between multi-material solutions when considering joining is presented, displaying the benefit of using MJTO when generating advanced multi-material designs.