Symmetric formulation of coupled BEM/FEM in solving responses of submerged elastic structures for large degrees of freedom

This work presents a symmetric formulation for the coupling of boundary element method (BEM) with finite element method (FEM) to compute responses of submerged elastic structures in a heavy acoustic medium. The acoustic loading derived from BEM is formulated in a symmetric complex matrix. The symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle, which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals. The structural equation is represented by FEM. The fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods. Consequently, the computational efficiency of the proposed coupled FEM/BEM is significantly increased. The proposed method involving 20000 degrees of freedom can be implemented on a personal computer. Numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force.