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A multi-material level set-based topology and shape optimization method
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DOI：10.1016/j.cma.2014.11.002.png)
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Abstract
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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. (C) 2014 Elsevier B.V. All rights reserved.
Keywords:
Topology optimization
Shape optimization
Multiple materials
Level set
Topology description model
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