Simplified Solution for Thin Plates Responses Using Beams Theory with Repetitive Boundary Conditions

In this study, a semi-analytical method is suggested for the analysis of thin plates. Various methods such as superposition, finite element, and integral transform have been applied to obtain solutions for thin plates. In this study, a simplified method has been proposed through an extension from the classical beam theory to solve plates, which is easier to apply yet relatively accurate. The method uses shape functions obtained from beam solutions having similar boundary conditions. The shape functions are used to approximate the displacement profile of the plate. Galerkin’s method is then applied to obtain the analytical solution of plate deflection. This involves evaluating integrals, which must be computed only once, and the values can be used later. The proposed moment and deflection coefficients are compared with that available in the literature. The results have been compared with previously reported solutions. The maximum error in the case of displacement of a simply supported plate was found to be 1.35% only. The shape functions and the values of integrals corresponding to various boundary conditions have been presented. Plates of various sizes and having various boundary conditions may be analyzed using the proposed closed-form solution for moment and shear. In addition, accurate deflection measurement of thin plates by other methods can be difficult and time-consuming. Therefore, this study explored analytical solutions that may provide a relatively accurate solution for thin plates with comparatively less computational effort.