Maximization of the fundamental eigenfrequency using topology optimization based on multi-material level set method

A multi-material structure that is composed of several different material properties is promising for achieving an ideal functionality that can outperform a single material structure. In the course of automotive design, the combination of lightweight and stiff materials can reduce the weight of a car body without sacrificing its performance. This paper proposes a multi-material topology optimization (MMTO) framework for the eigenfrequency maximization problem based on the Multi-material level set (MMLS) based topology optimization. The key idea of MMLS is to use M level set functions to represent M material regions and one void region without overlap. To demonstrate the proposed method, first, we formulate an MMTO problem for maximizing the eigenfrequency based on the shape representation by the MMLS method. Next, we derive the topological derivatives of multiple materials in the eigenfrequency problem and construct an optimization algorithm in which the level set functions are evolved by solving a reaction–diffusion equation (RDE) based on the topological derivatives. Several numerical examples are provided to validate the proposed methodology.