The fundamental solution of Mindlin plates resting on an elastic foundation in the Laplace domain and its applications

The aim of this study is to investigate the method of fundamental solution (MFS) applied to a shear deformable plate (Reissner/Mindlin’s theories) resting on the elastic foundation under either a static or a dynamic load. The complete expressions for internal point kernels, i.e. fundamental solutions by the boundary element method, for the Mindlin plate theory are derived in the Laplace transform domain for the first time. On employing the MFS the boundary conditions are satisfied at collocation points by applying point forces at source points outside the domain. All variables in the time domain can be obtained by Durbin’s Laplace transform inversion method. Numerical examples are presented to demonstrate the accuracy of the MFS and comparisons are made with other numerical solutions. In addition, the sensitivity and convergence of the method are discussed for a static problem. The proposed MFS is shown to be simple to implement and gives satisfactory results for shear deformable plates under static and dynamic loads.