An isoparametric quadratic boundary element for coupled stretching-bending analysis of thick laminated composite plates with transverse shear deformation

Recently, we derived the Green's function for an infinite thick laminated composite plate subjected to concentrated forces and moments. By serving this Green's function as the fundamental solutions, in this paper for the first time we develop the associated boundary element method (BEM), which is applicable to general problems of thick laminated plates with various types of deformations. For example, the in-plane stretching and out-of-plane bending deformations may be coupled together, which occurs for the unsymmetric laminated composite plates. Besides, the transverse shear deformations are also incorporated based upon the first order plate theory. To complete the entire development of the proposed BEM, all the involved issues, such as the boundary integral equations, the fundamental solutions and their derivatives, the mathematical formulation for the selected isoparametric quadratic boundary element, and the treatments of singular integrals are elaborated in this paper. The calculations of complete solutions at boundary or internal points are provided as well. The accuracy and efficiency of the proposed BEM are demonstrated through numerical examples, which show that it outperforms the conventional finite element method and is applicable for general thick laminated plates with unrestricted coupling effects.