Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions

In this study, we develop an approximate formulation for a generalized form of the biharmonic problem based on pseudospectral meshless radial point interpolation (PSMRPI). The boundary conditions are considered as simply supported or clamped, with application to the theory of static analysis of thin-plates. The rigorous steps to analyze such problem are defining the high order derivatives, implementing multiple boundary conditions especially when the geometry of the domain of the problem is complex. In PSMRPI method the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. Furthermore, it is observed that the multiple boundary conditions can be imposed by applying PSMRPI on nodal points near the boundaries of the domain. The main results on the generalized biharmonic problem are demonstrated by some examples to show the validity and trustworthiness of PSMRPI technique. Also, a comparison with the previously standard studied method for the biharmonic problem is done.