Fundamental solution and boundary element analysis of thick plates on Winkler foundation

Abstract

This paper introduces for the first time a full derivation of a fundamental solution and boundary integral equations for thick Reissner plates resting on a Winkler elastic foundation, where the effect of transverse normal stresses resulting from the foundation reaction on the plate surface has been considered. The fundamental solution is derived by means of Fourier and Hankel integral transforms in terms of complex Bessel functions. Reduction of domain integral loading terms is provided for cases with uniformly distributed loadings, and concentrated shear forces. Case studies, with known analytical solutions, were analyzed using the developed theory, and it has been shown that the given formulations provide a very accurate solution for a wide range of plate thickness.