A multi-material level set-based topology and shape optimization method

This paper proposes a new Multi-Material Level Set (MM-LS) topology description model for topology and shape optimization of structures involving multiple materials. Each phase is represented by a combined formulation of different level set functions. With a total number of M level set functions, this approach provides a representation of M materials and one void phase (totally M+1 phases). The advantages of the proposed method include: (1) it can guarantee that each point contains exactly one phase, without overlaps between each two phases and redundant regions within the design domain; (2) it possesses an explicit mathematical expression, which greatly facilitates the design sensitivity analysis; and (3) it retains the merits of the level set method, including smooth boundary and distinct interface. A parametric level set method is applied to evolve the topology and shape of multi-material structures, with a high computational efficiency. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.