The analysis of a rigid rectangular plate on a transversely isotropic multilayered medium

A semi-analytical method is developed for the analysis of a rigid rectangular plate on a transversely isotropic multilayered medium. Based on the governing equations of elasticity in Cartesian coordinates, transfer matrices for a single layer are deduced through a double Fourier transform and a Laplace transform. The transfer matrix solution of a multilayered medium is subsequently obtained with the consideration of the continuity conditions between two adjacent layers. By the application of the mixed boundary conditions of the contact problem, a pair of 2-D dual integral equations are derived, which are further converted to linear equations by means of the Jacobi orthogonal polynomials. The results of numerical calculation carried out by the corresponding computer program agree well with those obtained from the FEM software ABAQUS. Other numerical examples are presented to elucidate the influence of transversely isotropy, thickness and stratification of the medium.