A Pareto-optimal Approach to Multi-material Topology Optimization

As additive manufacturing expands into multi-material, there is a demand for efficient multi-material topology optimization, where one must simultaneously optimize the topology, and the distribution of various materials within the topology. The classic approach to multi-material optimization is to minimize compliance or stress while imposing two sets of constraints: (1) a total volume constraint, and (2) individual volume-fraction constraint on each of the material constituents. The latter can artificially restrict the design space. Instead, the total mass and compliance are treated as conflicting objectives, and the corresponding Pareto curve is traced; no additional constraint is imposed on the material composition. To trace the Pareto curve, first order element sensitivity fields are computed, and a two-step algorithm is proposed. The effectiveness of the algorithm is demonstrated through illustrative examples in 3D.