Topology optimization of frequency responses of fluid-structure interaction systems

This paper presents a topology optimization method for the frequency response of a multiphysics system involving fluid-structure interaction. The finite element analysis of the system is carried out based on the us/pf formulation. The structural domain is governed by the linear equation of elasticity and expressed in terms of the displacement, us, and the fluid domain is described by Helmholtz equation via the primary variable of pressure, pf. The coupling conditions are the equilibrium and kinematic compatibilities at the fluid-structure interface. The optimization procedure used in this work is based on the bi-directional evolutionary structural optimization (BESO). Due to the binary characteristics of the BESO method of adding/removing material, the methodology proposed here circumvents some problems faced by the traditional density based optimization methods, especially concerning the fluid-structure interface during the optimization process. The proposed methodology can be applied to various engineering problems such as noise reduction in passenger compartments in automobiles and aircraft, and vibration control of submerged structures. Several numerical examples are presented demonstrating that the proposed BESO method can be used for the topology optimization of these kinds of multiphysics problems effectively and efficiently for 2D and 3D cases.