MFS with RBF for Thin Plate Bending Problems on Elastic Foundation

In this chapter a meshless method, based on the method of fundamental solutions (MFS) and radial basis functions (RBF), is developed to solve thin plate bending on an elastic foundation. In the presented algorithm, the analog equation method (AEM) is firstly used to convert the original governing equation to an equivalent thin plate bending equation without elastic foundations, which can be solved by the MFS and RBF interpolation, and then the satisfaction of the original governing equation and boundary conditions can determine all unknown coefficients. In order to fully reflect the practical boundary conditions of plate problems, the fundamental solution of biharmonic operator with augmented fundamental solution of Laplace operator are employed in the computation. Finally, several numerical examples are considered to investigate the accuracy and convergence of the proposed method.