Topology optimization for the design of acoustic cloaking structure considering a self-supporting property

Abstract

In this research, we propose a topology optimization method for obtaining optimized structures satisfying a self-supporting property. First, we propose an artificial physical field that can detect structural components lacking the self-supporting property. Next, a level set-based topology optimization method is introduced, and we formulate the optimization problem, where the geometrical constraint function is defined with the artificial physical field. As a representative example of the optimization that requires the self-supporting constraint, we target an acoustic cloaking problem, and an objective function is defined with an acoustic pressure. The explicit formula of the design sensitivity is offered, which is based on the concept of the topological derivative. Several numerical examples are offered to confirm the validity and effectiveness of the proposed method. We show the characteristic of the proposed artificial physical field and conduct topology optimization for an acoustic cloaking structure without any unsupported structures.