With the availability of multi-material additive manufacturing, topology optimization of a multi-material structure and the selection of candidate materials become increasingly important. This paper aims to develop a new multi-material topology optimization algorithm and propose the guidelines for the selection of candidate materials from the database. The multimaterial design variables and their inequality relationship are built on volume fractions of multiple materials within each element. The multi-material design variables are relaxed and multiple floating projection constraints simulate their discrete constraints by pushing design variables towards 0 or 1. Meanwhile, their inequality relationship is enforced by their variation limits. The proposed multi-material topology optimization algorithm can be applied to the compliance minimization problem constrained by a single mass or multiple volumes, as demonstrated in numerical examples. This paper mainly focuses on a single mass constraint, and 2D and 3D numerical examples systematically demonstrate that an optimized design under a mass constraint achieves a lower compliance when more materials appear in the final design simultaneously. Furthermore, we establish an approach to predict the inclusion or exclusion of a material from the final design, and propose the conditions for the co-existence of candidate materials, which guide users to select candidate materials from the database. (C) 2021 Elsevier B.V. All rights reserved.
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