Thin rectangular plates under axial point loading: Accuracy of the classical single Fourier series solution for stresses

The purpose of this article is to clarify certain ambiguities associated with commonly adopted solution strategies of the problem of thin rectangular plates subjected to equal and opposite colinear point loads. The problem is treated as a plane-stress problem where the boundary conditions are prescribed exclusively in terms of tractions. Both an elaborate exact solution and a simplified approximate Single Fourier Series (SFS) solution are employed, shedding light on the accuracy of the latter. This is accomplished, first, by showing that the error implicit in the sine single-Fourier series solution becomes significant for column plates, and, secondly, by re-evaluating the stress distribution at various cross-sections away from the compressed sides, through the application of a truly exact solution to the problem at hand, in which the free-edge conditions are precisely fulfilled. It is shown that the restrictions usually associated with the SFS technique may not be severe and that a wider range of plate shapes with free vertical sides could be amenable to analysis utilizing this simple approximate scheme.

Automated summary

This article aims to clarify ambiguities in common solution strategies for thin rectangular plates subjected to colinear point loads. It compares an exact solution with a simplified Fourier Series solution, showing the limitations of the latter and the potential for wider applicability to plate shapes with free vertical sides.