On the Generation of Tuned Test Problems for Stress Concentrations

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. Here we offer a means of constructing such test problems for stress concentrations within boundaries that have local constant radii of curvature. These problems are tuned to their originating applications by sharing the same global geometries and having slightly higher peak stresses and stress gradients. Consequently, they are incrementally more challenging to solve with finite elements than their originating applications. They also have exact solutions. Thus, a precise determination can be made of the errors incurred in their finite element analysis.