Eigenanalysis for membranes with stringers using conventional BEM in conjunction with SVD technique

Abstract

It is well known that either the multi-domain boundary element method (BEM) or the dual BEM can solve boundary value problems with degenerate boundaries where double values are defined, i.e., two portions of boundary meet together with a zero thickness. In this paper, the eigensolutions for membranes with stringers are obtained in a single domain by using the conventional BEM in conjunction with the SVD technique. By adopting the SVD technique for rank revealing, the nontrivial boundary mode can be detected by the successive zero singular values which are not due to the degeneracy of degenerate boundary. The boundary modes are obtained according to the right unitary vectors with respect to the zero singular values in the SVD. Three examples, a single-edge stringer, a double-edge stringer and a central stringer in a circular membrane, are considered. The results of the present method, are compared with those of the multi-domain BEM, the dual BEM, the DtN method (Dirichlet to Neumann), the FEM (ABAQUS) and analytical solutions if available. Good agreement is obtained. The goal to deal with the eigenproblem in a single domain without hypersingularity is achieved.