Finite element treatment of exterior fluids in fluid‐structure interaction problems

Abstract

Several finite element solution approaches are described for fluid‐structure interaction problems involving an exterior fluid. The specific problems of interest are those of acoustic radiation and scattering from submerged elastic structures subjected, respectively, to internal time‐harmonic mechanical loads or an incident time‐harmonic wavetrain. These problems can be solved by combining a finite element model of the structure with a fluid loading computed using finite element, boundary element, infinite element, or decoupling techniques. Formulations are presented and compared for fluid domains modeled using an added mass matrix, the doubly asymptotic approximation (a decoupling technique), explicit fluid finite elements, and the Helmholtz exterior integral equation. With the exception of the integral equation treatment, all these fluid‐loading approaches can be implemented using the standard finite element modeling capabilities available in structural analysis computer codes such as NASTRAN. The most accurate fluid treatment is obtained with the Helmholtz integral equation although this is at somewhat greater computational cost than that required using the less precise approaches.