Singularity

In structural mechanics and finite element analysis (FEA), the term "singularity" refers to a situation where the stress or strain distribution near a point in the model becomes infinitely large or changes by an unexpected amount. Such singularities typically occur near geometric irregularities such as corners, edges, beads, cracks or load applications.

In practice, singularities are often a cause for concern as they indicate possible weak points in the structure that could lead to failure. However, not all singularities are realistic or physically significant. Sometimes they are the result of insufficient discretization (too few or inappropriate element types) or a simplified load or boundary condition approach in the FE model.

To better understand singularities in FEM analysis and to assess their impact on the structure, it is important to review the quality of the model, the discretization, the types of elements used, and the application of loads and boundary conditions. Refinement of the FE mesh, adjustment of element types or more accurate modeling of boundary conditions can help to reduce the effects of singularities and increase the accuracy of the FEM results.

Singularities in the model should be avoided if possible. If this is not successful, the influence of the network should be suppressed by means of appropriate linearization (e.g. interior linearization or surface extrapolation). The user must then ensure that the stress value calculated in this way is suitable for proof of strength.89