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Stress singularities, stress concentrations and mesh convergence Stress singularities, stress concentrations and mesh convergence June 2, 7 Comments Written by M. It relies on discretizing a continuum domain into finite elements.
The accuracy of the Conclusions of stress 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.
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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. When do they pose for concern? How should we, as FE analysts, deal with them?
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 results will be fine!
This is an immediate consequence of St. Perhaps one of the most important principle in FEA as it validates FEA results even with the presence of singularities. Further away from the disturbance the results will not be perturbed.
Typically, as far away as the size of the disturbance. Uniform tension load applied to specimen. The stress distribution at the vicinity of the applied load is not uniform.
However, the stress becomes uniform some distance away of the applied load . Therefore, if we are not interested in the stresses near the singularity point, we should only be concerned about transmitting the resultant load P to the specimen.
It does not matter if this is done through a point load or a pressure load, as far as the resultant is transmitted the stresses at the central section will be correct.
A single point load leads to stress singularities whereas an edge pressure results in a uniform stress field.
As you can see, far away from the point load singularity the stress field is uniform despite of the local singularity. Note that pressure load do not cause point singularities, this is because the pressure attribute is converted by the solver into a set of point loads along the nodes of the edge in a consistent fashion that do not cause a singularity.
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In both cases this corner leads to a singularity. No matter how much we refine the mesh, the stresses will not converge at the vicinity of the corner. The local singularity and its effect is shown in the following image.
The image above is a contour of the global vertical stress over the nominal applied stress at the top.
The L structure has been modelled as a plane stress model, typical aluminium properties have been assigned and the right most edge nodes have been restrained.From the Chair The UNC Department of Psychiatry is committed to excellence in our missions: clinical service, teaching, and research, .
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