静電容量型超音波トランスデューサの最適構造設計法 : レベルセット法に基づく等断面形状制約付きトポロジー最適化

Abstract

Capacitive micromachined ultrasonic transducers (cMUTs) are a new type of transducer with applications in medical ultrasound equipment. This paper presents a topology optimization method for the structural design of cMUTs, in which the outlines of target structures are implicitly represented using the level set method, and uniform cross-section surface constraints are taken into account. First, the optimization problem that addresses the design requirements of the cMUT is formulated. Second, basic details of the level set-based topology optimization method are briefly discussed. Based on the concept of the Tikhonov regularization method, the topology optimization method considering a uniform cross-section surface constraint is formulated. Next, based on this formulation and the level set method, a topology optimization algorithm is constructed where the Finite Element Method is used when solving the equilibrium equations and the level-set equation. Finally, two- and three-dimensional examples are provided to confirm the validity and utility of the proposed topology optimization method.