Green's function for thick laminated composite plates with coupled stretching-bending and transverse shear deformation

In this paper, the Green's function of a thick laminated composite plate is derived for the first time in the literature. The plate can be unsymmetric with respect to the mid-plane such that the coupling of in-plane stretching and out-of-plane bending deformations occurs. Also, the plate is thick enough that the transverse shear deformation cannot be ignored. Through the plane wave decomposition method, the partial differential governing equations based upon the first order shear deformation plate theory can be reorganized into the ordinary differential equations in terms of the transformed variable. With the governing equations reorganized into matrix form, the Green's functions are expressed in terms of matrix exponential. Through eigen-decomposition, the matrix exponential including its related integrals can be evaluated explicitly. The explicit solutions of Green's functions in transformed domain are obtained accordingly. In order to improve the accuracy and efficiency of numerical integration for the required transform integrals, a special quadrature rule which can eliminate the integral singularity is suggested. To have a fair verification and to extend the applicability of newly derived Green's functions, the associated boundary element method is also introduced in this study.