Ritz variational method for bending of rectangular kirchhoff plate under transverse hydrostatic load distribution

In this study, the Ritz variational method was used to analyze and solve the bending problem of simply supported rectangular Kirchhoff plate subject to transverse hydrostatic load distribution over the entire plate domain.The deflection function was chosen based on double series of infinite terms as coordinate function that satisfy the geometric and force boundary conditions and unknown generalized displacement parameters.Upon substitution into the total potential energy functional for homogeneous, isotropic Kirchhoff plates, and evaluation of the integrals, the total potential energy functional was obtained in terms of the unknown generalized displacement parameters.The principle of minimization of the total potential energy was then applied to determine the unknown displacement parameters.Moment curvature relations were used to find the bending moments.It was found that the deflection functions and the bending moment functions obtained for the plate domain, and the values at the plate center were exactly identical as the solutions obtained by Timoshenko and Woinowsky-Krieger using the Navier series method.