A Shape and Topology Optimization Method Incorporating Level Set Boundary Expressions for Vibration Problems

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For the design of mechanical structures, vibration characteristics such as eigenmodes and eigenfrequencies are important factors which determine the dynamic performance. This paper propose a topology optimization method for vibration problems based on level set structural boundary expressions and the use of a fictitious interface energy. First, we briefly discuss the basic details of the topology optimization method incorporating level set-based structural boundary expressions. The topology optimization method is then applied to the problem of maximizing the lowest eigen-frequency. Next, an optimization algorithm for the proposed method is constructed using the Finite Element Method (FEM). Finally, to confirm the validity and utility of the proposed topology optimization method, two-dimensional and three-dimensional numerical examples are provided.

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