Solution of fluid–structure interaction problems using a coupled finite element and variational boundary element technique

Abstract

This work is concerned with the numerical modeling of elasto-acoustic problems applied to thin shells and specifically curved plates. A finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem. This solution to the acoustic problem, proposed by Mariem and Hamdi [J. B. Mariem and M. A. Hamdi, Int. J. Num. Methods. Eng. 24, 1251–1267 (1987)], is implemented using high-order isoparametric elements, and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies. These techniques include a reduction in the problem size through the use of symmetry and, more importantly, the interpolation of the fluid impedance matrix within the frequency regime. The advantages in using this variational formulation are, first, the manner in which a highly singular integral operator is made amenable to numerical approximation, second, its application to nonclosed thin shells, and, third, its numerical implementation leads to the formulation of a symmetrical fluid matrix.