Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

TLDR

Acoustic–structure interaction couples pressure and displacement fields via Helmholtz and elasticity equations, but conventional surface‑coupling integrals prevent free material redistribution in topology optimization because boundaries are not explicitly represented. The study develops a gradient‑based topology optimization formulation that solves acoustic–structure interaction problems without explicit boundary interface representation by employing a mixed finite element approach. The method uses a mixed finite element formulation with displacement and pressure as primary variables, varying mass density, shear, and bulk moduli spatially, and implements topology optimization as a standard density approach, which is validated on several two‑dimensional acoustic–structure problems. When the elastic shear modulus is set to zero, the mixed formulation reduces to the Helmholtz equation. © 2006 John Wiley & Sons, Ltd.

Abstract

Abstract The paper presents a gradient‐based topology optimization formulation that allows to solve acoustic–structure (vibro‐acoustic) interaction problems without explicit boundary interface representation. In acoustic–structure interaction problems, the pressure and displacement fields are governed by Helmholtz equation and the elasticity equation, respectively. Normally, the two separate fields are coupled by surface‐coupling integrals, however, such a formulation does not allow for free material re‐distribution in connection with topology optimization schemes since the boundaries are not explicitly given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u / p ‐formulation). The Helmholtz equation is obtained as a special case of the mixed formulation for the elastic shear modulus equating to zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modelling approach, the topology optimization procedure is simply implemented as a standard density approach. Several two‐dimensional acoustic–structure problems are optimized in order to verify the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.