Boundary integral equations for general laminated plates with coupled stretching–bending deformation

Abstract

The boundary integral equations for the stretching–bending coupling analysis of general laminated plates are derived in this paper with the aid of the reciprocal theorem of Betti and Raleigh. No restriction is placed on the location of the point load or moment, and so it can be an internal or external point or a smooth or non-smooth boundary point. The fundamental solutions derived from Green’s function for an infinite laminated plate subjected to concentrated forces/moments are presented in the complex matrix form. Through the use of some identities converting complex form to real form, the free term coefficients, which are important for the boundary integral equations, are obtained explicitly and expressed in the real form. Alternative formulae for calculating the free term coefficients are also derived using five rigid body movements. By using the explicit real expressions obtained recently for the Stroh-like formalism of coupled stretching–bending analysis, the free term coefficients are further reduced to the cases of isotropic plates and are then compared with known expressions published in the literature. Since stretching and bending decouple for isotropic plates, comparison is made separately for the in-plane problem and plate bending problem, and it is shown that the boundary integral equations derived in this paper agree with previous results for these two special cases.