Analysis of Corner Supported Plates Under Symmetrical Loading

In this study, a Ritz method-based solution of the corner supported thin rectangular plate under different symmetrical loading is presented. The load can be uniformly distributed, symmetrically applied point, patched, or line loads or any type of load applied symmetrically about the plate axes. A two-dimensional polynomial that satisfies the essential boundary conditions (zero deflection at the corners) is proposed to approximate the deflection of the plate. The results are found to be in an excellent agreement with the literature and finite element results. For cases of point loads, however, the proposed polynomial as well as the previously proposed methods in the literature are not capable of capturing the singularity under the point loads. As a remedy to this problem, the proposed polynomial expression is strengthened with the fundamental solution. The strengthened polynomial is found to be able to capture the singularity as well as to accurately satisfy the natural boundary conditions at the free edges.