A non-singular fundamental solution for boundary element analysis of thick plates on Winkler foundation under generalized loading

Abstract

This paper introduces a new generalized non-singular fundamental solution for boundary element analysis of thick plates on a Winkler elastic foundation for different cases of characteristic equation roots including the case with equal roots, where the corresponding kernel functions have been derived using a practical approach. The terms of kernel functions in domain loading integrals have been reduced to boundary integrals for cases with uniformly and linearly distributed loading. Boundary integral expressions have also been derived for generalized loading cases with line shear forces and bending moments acting on arbitrary curves defined on the plate midplane. Different case studies, with known analytical solutions, were analysed using the developed theory, and it has been shown that the given formulations provide a very accurate solution for different types of loading.