On the design and analysis of simply supported and clamped thick rectangular plates

Abstract

The finite difference method, although well known as an efficient numerical method, was applied in the past, in the case of plate problems, only for the solution of thin plates. In the present study, the suitability of the method for problems involving thick plates is studied. The finite difference method as applied here is a modified finite difference approach to the ordinary finite difference method generally used for the solution of thin plate problems. Thin plates are treated as a particular case of the corresponding thick plates. The method is first applied to investigate the behaviour of clamped, square isotropic homogeneous thick plates. After the validity of the method is established, it is then extended to the solution of similar problems for simply supported square plates. Once the solution for a thick plate with a particular plate aspect ratio and boundary condition is obtained using a limited number of mesh sizes, a more refined solution to investigate the accuracy and convergence of the problem is then extended by providing more detailed functions satisfying the mesh sizes generated automatically by a computer program. Whenever possible results of the present method are compared with existing solutions in the technical literature obtained by much more laborious numerical techniques, and close agreements are found. The submatrices involved in the formation of the finite difference equations from the governing differential equations are generated directly by the computer program. Simplicity in formulation and quick convergence are the obvious advantages of the method in comparison with other numerical methods requiring extensive computer facilities.