Mathematical Model for the Deflection of Rectangular Stiff Plate

Numerical solutions to various types of plate structures are indispensible in engineering since it provides approximate solutions to mathematically expressed equation governing a plate. On the other hand, analytical solution provides exact solution to plate bending problems but has restrictions in areas of practical interest. In this study, an improved finite difference method (IFDM) which is a numerical method was used to transform the governing differential equation of a rectangular stiff plate on elastic foundation into improved finite difference coefficients using the central difference method on the discretised plate on elastic foundation. The coefficients obtained from the numerical method were applied into the governing differential equation of the rectangular stiff plate on elastic foundation to obtain the mathematical model for deflection of the plate. Thereafter, 25 interior nodal points of the plate were considered, and the improved finite difference coefficients were evaluated at nodal points to obtain a set of simultaneous linear equations using the boundary conditions for an all edge clamped plate CCCC.