Stress singularities in classical elasticity–I: Removal, interpretation, and analysis

Abstract

This review article has two parts, published in separate issues of this journal, which consider the stress singularities that occur in linear elastostatics. In the present Part I, after a brief review of the singularities that attend concentrated loads, attention is focused on the singularities that occur away from such loading, and primarily on 2D configurations. A number of examples of these singularities are given in the Introduction. For all of these examples, it is absolutely essential that the presence of singularities at least be recognized if the stress fields are to be used in attempts to ensure structural integrity. Given an appreciation of a stress singularity’s occurrence, there are two options open to the stress analyst if the stress analysis is to actually be used. First, to try and improve the modeling so that the singularity is removed and physically sensible stresses result. Second, to try and interpret singularities that persist in a physically meaningful way. Section 2 of the paper reviews avenues available for the removal of stress singularities. At this time, further research is needed to effect the removal of all singularities. Section 3 of the paper reviews possible interpretations of singularities. At this time, interpretations using the singularity coefficient, or stress intensity factor, would appear to be the best available. To implement an approach using stress intensity factors in a general context, two types of companion analysis are usually required: analytical asymptotics to characterize local singular fields; and numerical analysis to capture participation in global configurations. Section 4 of the paper reviews both types of analysis. At this time, methods for both are fairly well developed. Studies in the literature which actually effect asymptotic analyses of specific singular configurations will be considered in Part II of this review article. The present Part I has 182 references.