Structural Shape and Topology Optimization in a Level Set Based Implicit Moving Boundary Framework

In this paper we present a new framework to approach the problem of structural shape and topology optimization. We use a level set method with an implicit moving boundary model. As a boundary optimization problem, the structural boundary description is implicitly embedded in a scalar function as its “iso-surfaces.” Such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure. Furthermore, by using a simple Hamilton-Jacobi convection equation, the movement of the implicit moving boundaries of the structure is driven by a transformation of the objective and the constraints into a speed function that defines the level set propagation. The result is a 3D structural optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation, comparing favorably with other methods based on explicit boundary variation or homogenization in the literature. We have developed a number of numerical techniques for an efficient and robust implementation of the proposed method. The method is tested with several examples of a linear elastic structure that are widely reported in the topology optimization literature.

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