Multi-Material Multi-Joint Topology Optimization: A Unified Approach
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In this research, a methodology and computational tool that solves multi-material topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials was developed. Multi-material topology optimization is a design optimization technique that can determine the optimal distribution of multiple materials within a domain and is typically used to create lightweight designs superior to those created by conventional single-material topology optimization. The usefulness of the technique is limited, however, since all current approaches for multi-material topology optimization assume that all materials are perfectly fused together as a single piece. Since the ideal geometry of a real-world, multi-material design is mutually dependent on the configuration of joints, it follows that current approaches are insufficient for creating practical multi-material designs. The presented methodology uses a novel decomposition approach to determine both the optimal geometry of a multi-material design as well as the optimal joint design along the interfaces. By decomposing the problem into two simpler subproblems that are solved iteratively, gradient-based optimization techniques can be used, facilitating the solution of large problems that cannot be considered by combinatorial approaches including genetic algorithms. Since the joining interfaces are interpreted directly from multi-material topology optimization results, the shape of the interfaces and the quantity of joints connecting dissimilar materials do not need to be defined by the user a priori. By changing the design variable definition in each subproblem, the computational tool is able to solve both subproblems using the same finite element model provided by the user. Once optimization begins, all model preparation tasks are completed automatically by the tool and no further input is needed from the user. The methodology and computational tool were verified with three numerical examples. In each example, the tool optimized the geometry of a multi-material design to maximize stiffness while also minimizing the cost of required joints. This study was the first of its kind to not only consider and optimize joints in multi-material topology optimization, but was also the first study to consider multiple types of joints in a joining optimization process.