Special finite elements for the analysis of stress concentrations and singularities

Abstract

In matrix formulations, each region of stress concentration requires the use of a large number of small conventional finite elements, and often, the advantage of a fine mesh can be overcome by numerical errors. The situation can be particularly difficult in the presence of elastic stress singularities. A method has been developed to overcome this difficulty; a fairly large element replaces a large number of the conventional small elements in each region of concentration. The displacement or stress description of this large element includes terms that represent the nature of the local concentration. A method for developing such a large finite element and applying it is described and illustrated by typical examples. Some of the solutions are compared with conventional finite element solutions.