Moment and Stress Analysis Solutions of Clamped Rectangular Thick Plate

The bending solutions of rectangular thick plate with all four edges clamped (CCCC) were investigated in this study. The basic governing equations used for analysis are based on third-order shear deformation plate theory analysis under uniformly distributed load. Using a formulated total potential energy equation, the three coupled general governing differential equations for the determination of the out of plane displacement and shear deformations rotation along the direction of x and y coordinates were obtained. These equations as obtained are solved simultaneously after minimization to determine the coefficients of displacements of the plate and other the mentioned functions. By solving these equations, the analytic solutions of rectangular thick plate with all four edges clamped were derived. From the formulated expression, the formula for calculation of the maximum deflection, moment, stress and in-plane displacements were deduced. The proposed method obviates the need of shear correction factors, which is associated with Mindlin’s theory (FSDT) for the solution to the problem. Moreover, numerical comparison shows the correctness and accuracy of the results.