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Stress singularities, stress concentrations and mesh convergence

1. Introduction
The FEM (Finite Element Method) is a way of obtaining a of finding a solution to a physical problem. It relies on discretizing a continuum domain into finite elements. The accuracy of the solution greatly depends on the number of elements used to represent the physical domain. As we progressively refine the mesh, the solution improves and given enough iterations it converges towards a specific result. If there is an analytical solution for the given problem, the mesh refinement procedure will converge towards the exact solution.
However, there are situations where the solution does not converge with mesh refinement. Stress singularities are one of these situations. This article puts its focus on stress singularities and stress concentrations. What are they? When do they pose for concern? How should we, as FE analysts, deal with them?

2. Stress singularities
In structural analysis, we are mainly concerned about displacements and their derivatives - the stresses. A stress singularity is a point of the mesh where the stress does not convergence towards a specific value. As we keep refinement the mesh, the stress at this point keeps increasing, and increasing, and increasing... Theoretically, the stress at the singularity is infinite.
Typical situations where stress singularities occur are the appliance of a point load, sharp re-entrant corners, corners of bodies in contact and point restraints. As you can see, stress singularities are a common situation in FEA. The analyst must use his knowledge to determine the possible singularity locations and see if they are of importance for the model or not.
Although stress at these singularities is infinite, this does not mean that the model results are incorrect overall. First of all, the displacements are correct even at the singularity point. On the contrary, the stress at the singularity will pollute the stress results near the singularity, however some distance away from the singularity the stress re

Categories: Information Technology
Topics: stress concentrations and mesh convergence, stress singularities

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