Application of variational methods to a rectangular clamped plate problem

摘要

The present paper deals with the variational approach for solving a clamped rectangular plate under a uniform load. The increasing use of composite materials for plate-type structures intensified the need for solutions of rectangular plates. The variational approach has a broad range of applications in solid mechanics. The methods used to solve the problem consider the minimum total potential energy approach. The maximum deflection is obtained for a square plate by the Ritz, Galerkin and Kantorovich methods. The aim of this paper is to find an approximate solution of higher accuracy. Numerical results for various components of stresses are found and plotted in the form of curves. The results obtained by various methods are compared with those reported earlier. The results show reasonable agreement with the known results, but with a simple and practical approach. The physical aspect of the concept is the immediate use of these results in solid and structural mechanics.