Dual boundary element analysis of wave scattering from singularities

Abstract

The dual boundary element method is used to obtain an efficient solution of the Helmholtz equation in the presence of geometric singularities. In particular, time-harmonic waves in a membrane which contains one or more fixed edge stringers (or cracks) are investigated. The hypersingular integral equation is used in the procedure to ensure a unique solution for the problem with a degenerate boundary. The method yields a solution for the entire membrane as well as the dynamic stress intensity factor. Numerical results are presented for a circular membrane containing a single edge stringer, two edge stringers and an internal stringer. Also, the first three critical wave numbers of the membrane with the homogeneous boundary condition are determined, and the dynamic stress intensity factors are found for problems with the nonhomogeneous boundary condition. Good agreement is found after comparing the results with exact solutions, and with results obtained using DtN-FEM and ABAQUS.