A BEM-based meshless method for plates on biparametric elastic foundation with internal supports Original Research Article

In this paper a BEM-based meshless method is developed for the analysis of plates on a biparametric elastic foundation which, in addition to the boundary supports, are also supported inside the domain on isolated points (a group of plies) and/or line supports (continuous plates). The presented method is achieved using the concept of the analog equation method (AEM) of Katsikadelis. According to this method the original governing differential equation is replaced by an equivalent problem for plates without internal supports not resting on an elastic foundation subjected to an “appropriate” fictitious load in addition to the transverse external loads under the same boundary conditions. The fictitious load is established using a technique based on BEM and approximated by radial basis functions series. The solution of the actual problem is obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. Thus, the kernels of the boundary integral equations are conveniently established and evaluated. The presented method has all the advantages of the pure BEM. To validate the effectiveness, accuracy as well as the applicability of the proposed method, numerical results of various example problems are presented.