Stress singularities are an inherent part of all FEA analyses and they are inevitable in the case of sharp re-entrant corners and edges as well as loads and fixtures that are applied to entities with zero surface area (such as edges and vertices).
In such locations, due to mathematical errors, the value of stress increase infinitely and therefore, the stresses cannot be read at the locations of stress singularity.
To get more information about stress singularity and methods to work around them, please see our following blog articles on Mesh Refinement for Stress Singularities Hot Spot Diagnostic and Locate Singularities by Detecting Hot Spots.
The same concept of singularity applies to the thermal simulations. A singularity can be created in the heat flux distribution plots at similar locations such as sharp re-entrant corners of the model.
A direct analogy between heat fluxes and stresses can be helpful in conceptualizing heat flux singularity. Similar to the fact that a model with sharp re-entrant edge in a structural stress analysis cannot have stress solution over the edge, a thermal analysis is unable to solve the heat flux solution in the sharp re-entrant edge. Instead of infinite values for heat flux, due to discretization errors, the FEA software show finite values for the heat flux distribution. However, the values of heat flux is only dependent on the element size at the vicinity of heat flux singularity and would increase by refining the mesh.
An example of heat flux singularity can be seen in the attached picture. A thermal simulation has been run and the distribution of heat flux is plotted. As seen in the picture, in this study the hot spot locations of heat flux coincide with the sharp re-entrant edges, and they appear to be caused by singularity. Therefore, the value of these stresses is meaningless.
The work-around for heat flux singularity is similar to stress singularity. The heat flux singularity only affect near by elements, therefore by reading the heat flux at a few elements away from the source of singularity, correct values of heat flux can be obtained. Another work-around is to remove the source of singularity, for example eliminating the sharp re-entrant edge by adding a fillet.
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