Application of finite difference method to the deflection of clamped and simply supported thick rectangular plates

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Variational methods are widely used for the solution of complex differential equations in mechanics, for which exact solutions are not possible. the finite difference method although well known as an efficient numerical method was applied in the past only for the solution of thin plates. in the present study, the suitability of the method for the solution of deflection of thick plates is studied for the first time. while there is major differences between thin plate and thick plate theories, the former can be treated as a particular case of the latter, when the centre deflection of the plate is less than or equal of the thickness of the plate. 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. in this thesis thin plates are treated as a particular case of the corresponding thick plates when the boundary conditions of the plates are taken into account. the method is first applied to investigate the behaviour for clamped, square isotropic homogeneous 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 a solution for a particular plate aspect ratio and boundary condition is obtained using a limited number of mesh sizes, a general solution of the problem to investigate accuracy and convergence was extended to rectangular thick plates by providing more detailed functions satisfying the