On the Generation of Tuned Test Problems for Stress Concentrations Induced by Shear Tractions

Abstract When stress concentration factors are not available in handbooks, finite element analysis has become the predominant method for determining their values. For such determinations, there is a need to know if they have sufficient accuracy. Tuned test problems can provide a way of assessing the accuracy of stress concentration factors found with finite elements. Previously, we offered a means of constructing such test problems for stress concentrations within boundaries that have local constant radii of curvature, and are subjected to tensile loading. Here we extend the means of construction for the same local geometry, but now with the stress concentrations being induced by shear loading. These new test problems are tuned to their originating shear applications by sharing the same global geometries and having slightly higher peak stresses. Consequently, they are a little more challenging to analyze with finite elements than their originating shear applications. These test problems also have exact solutions. Thus a precise determination can be made of the errors incurred in their finite element analysis. Given the increased challenge of these test problems, their errors are likely to serve as upper bounds on the errors incurred when their originating configurations are analyzed with the same set of finite element meshes.