Stability analysis of laminate plates by the boundary element method

A numerical analysis of laminate plate buckling, based on the boundary element method (BEM), is presented. Bending-stretching coupling is ignored and uniform in-plane edge loading is assumed. Integral equations containing an irreducible domain integral depending on the plate deflection are derived from a reciprocity relation using the fundamental solutions of the anisotropic plate bending problem. Boundary modelling is combined with deflection modelling over the plate so that three integral equations are approximated as a discrete system of equations forming an eigenvalue problem from which the critical load can be evaluated. This approach removes the need for integral equations involving the domain curvatures yielding directly the buckling mode of the plate. Linear discontinuous boundary elements as well as domain cells are employed combined with special schemes for the approximation of jump terms at corners. Singular integrals over elements containing the source point are evaluated from closed-form expressions derived through analytical integration. The C code implementing the solution algorithm is applied to several benchmark problems involving orthotropic plates and BEM predictions are compared with solutions available from the literature or obtainable through a general purpose finite element package. The reliability of the proposed analysis is established through further applications to laminate plates of general anisotropy.