On homogenous solutions of the problem of a rectangular cantilever plate bending

Abstract

The paper considers the method suggested by Papkovich for rectangular plates and its application for a cantilever plate bending under a uniform load. The required function of the bendings is chosen in the form of a sum of the corresponding beam function and a biharmonic function, which is a series in terms of unorthogonal eigenfunctions of the problem. The eigenfunctions satisfy the homogenous boundary conditions on the longitudinal edges (the clamped and the opposite ones). It is suggested to find series coefficients from the condition of the minimum residuals effect on the corresponding displacements of the transverse edges. It leads to an infinite system of linear algebraic equations for the required coefficients in the complex form. The coefficients of homogenous solutions were found for the cases in which the approximating series contained sequentially 2, 3,...,7 terms. The eigenvalues, the bendings of the edge opposite to the clamped edge, and the bending moments in the clamped section were calculated. Convergence of the reduction method and stability of the computational process were analyzed.