Plate bending analysis with variational finite difference methods on general grid

Abstract

A variational finite difference (FD) approach has been applied to solve plate bending problems on a general grid. Two methods of approximation have been considered. The general least squares FD method has been used on irregular rectilinear and curvilinear meshes and compared to the curvilinear FD method. The impact of different orders of approximation quality of both methods on the convergence and stability of the FD solutions on an irregular grid is illustrated on several square and circular plate examples where the exact solution could also be supplied. Of the methods considered, only the least squares FD method is stable when the regularity of the mesh is locally disturbed.