Improved computation of stress resultants in the p-Ritz method

Abstract

This paper highlights the problems encountered in bending and vibration analysis of thin plates when using the p-Ritz method for computing the stress resultants, especially the twisting moments and shear forces. In the p-Ritz method, products of mathematically complete two-dimensional polynomial functions and boundary polynomial equations raised to appropriate powers are used to approximate the displacements. This ensures the satisfaction of the geometric boundary conditions. However, it is found that the distributions of the twisting moment and shear forces contain unacceptable oscillations, and for plates with free edges these stress resultants do not satisfy the natural boundary conditions. A method to overcome the aforementioned problems is proposed here. The penalty function method is used to satisfy the natural boundary conditions and postprocessing of the stress resultants to eliminate the oscillations. Some examples of static and vibration problems of plates are presented to illustrate the effectiveness of the proposed strategy for overcoming the shortcomings inherent in the p-Ritz method.