Green’s function of anisotropic plates with unrestricted coupling and degeneracy, part 1: the infinite plate

Abstract

Green’s function of the infinite domain is determined for all types of nondegenerate and degenerate anisotropic plates with bending–extension coupling, and for various kinds of singularities including (i) concentrated forces and moments in both in-plane and normal directions and (ii) dislocations of the tangential and normal displacements and of the midplane slopes. Explicit analytical expressions of Green’s function are obtained in terms of the zeroth-order and higher-order eigenvectors. Higher-order eigenvectors occur in the various degenerate cases and may significantly affect the angular variation of Green’s function. Some familiar types of laminates, including all isotropic laminates and symmetric quasi-isotropic laminates, are degenerate or extra-degenerate. Since all previous works on Green’s functions of laminates assumed distinct eigenvalues, the results contain no higher-order eigenvectors. They are only valid in the relatively simple nondegenerate case, and are not applicable to any type of degenerate laminate.