In this presentation we address the problem of structural shape and topology optimization in a multi-material domain. A level set method is adapted as an alternative approach to the usual homogenization based methods of rule of mixtures for multi-material modeling. We generalize the level-set representation scheme by proposing a multi-phase level-set model. This “color” level set representation has its unique benefits: it is flexible to handle complex topologies; it yields a Hamilton-Jacobi PDE system for the design optimization; and it provides a natural setting for shape variation and geometric regularization. The result is a 3D topology/material optimization technique with outstanding fidelity of boundary representation and degree of automation. We also describe numerical techniques for efficient and robust implementation of the method, by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain, thus separating numerical calculations of the physical system from geometric evolution. The benefits and the advantages of the developed method are illustrated with several examples of mean compliance minimization of multi-material structures, optimal material design, and compliant-mechanism design.
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