A unified boundary element method for the analysis of sound and shell-like structure interactions. I. Formulation and verification

Abstract

A unified boundary element method (BEM) is developed in this paper to model both the exterior acoustic field and the elastic shell-like structure in a coupled analysis. The conventional boundary integral equation (BIE) for three-dimensional (3D) elastodynamics is applied to thin shell-like structures which can have arbitrary shapes and small thicknesses. The nearly singular integrals existing in the BIE when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently. For the exterior 3D acoustic domain, the Burton and Miller composite BIE formulation is employed to overcome the fictitious eigenfrequency difficulty (FED) and the thin-shape breakdown (TSB). Conforming C0 quadratic elements are employed in the discretization of the two sets of BIEs. The developed BIE formulations are valid for both radiation and scattering problems and for all wave numbers. Numerical examples using spherical and cylindrical shells, including nonuniform thickness and nondimensional wave numbers up to 12, clearly demonstrate the effectiveness and accuracy of the developed BEM approach.