Problems and remedy for the Ritz method in determining stress resultants of corner supported rectangular plates

This paper is concerned with the bending of corner supported rectangular plates under transverse uniformly distributed load. It is shown herein that the commonly used Ritz method does not predict accurate stress resultants, especially the twisting moment and the shear forces. Firstly, these stress resultants do not fully satisfy the natural boundary conditions, and secondly they exhibit oscillations in the distribution of the stress resultants in the plate domain and give rise to significant errors in the maximum values. As a remedy to the aforementioned problems, we propose the use of (a) the Lagrange multiplier method to ensure the satisfaction of the natural boundary conditions and (b) a surface-smoothing technique to post-process the solution to eliminate the oscillations in the distribution of stress resultants. To illustrate the effectiveness of the proposed strategy, we compare the solutions with those obtained by commercial finite element software. As an example, uniformly loaded, corner supported rectangular plates are used in the study.