Singularity Finite Elements for Plate Bending

Abstract

The elastic analysis of floor slabs using the finite element method encounters special difficulties at certain types of reentrant corners where classical plate theory predicts singular moments and shear forces. Examples are the corners of floor openings and the corner points of rectangular columns or shear cores. The nature of the stress singularities at these corners is discussed, and a family of special purpose hybrid stress plate bending elements is derived for use at these locations. These elements, which may be rectangular or L‐shaped, contain the appropriate singular moments as part of their assumed moment fields. The elements are tested on three example problems and the results are compared with those obtained using regular hybrid stress elements. Improved convergence and a better representation of the moment field are obtained with these special purpose elements. It is concluded that the more rapid convergence and additional accuracy justify the increase in computational effort.