This can be easily seen where the same total force is applied to the sponges in two different ways. Due to Saint-Venant’s-principle, which states that, if the distance from the load is large enough, two different but statically equivalent loads create essentially the same effect. If the area where the load is applied is not of interest, then it can be acceptable to use such a boundary condition. Since stress is force divided by area, applying a force at a single point will give an infinite stress. The most obvious way that a boundary condition can cause a singularity is when a force is applied to a single node. How can boundary conditions cause singularities? Let’s explore why this happens and how it can be avoided. Where there are abrupt changes in boundary conditions, such as a split line where a fixed constraint ends, this can also result in stress that continues to rise unrealistically and causes mesh convergence to fail. There is, however, another type of stress raiser in FEA models that is talked about less often and which can be more difficult to deal with. Singularities at corners are similar to cracks and the stress intensity factor can be calculated using the J-Integral, or considering the strain energy release rate – the energy dissipated during fracture. The location of these singularities can often be readily identified, excluded from convergence results and localized models used to predict the true stress in the features responsible. In any case, local yielding will limit the stress in such features. In the real world, there is likely to be a small radius on any internal corner, meaning the stress would not actually continue to rise. Singularities caused by stress-raising geometry such as holes and sharp internal corners are well understood. This produces nonsensical results and prevents mesh convergence. As the element size tends to zero, the stress will tend to infinity. As the mesh is refined, the increasingly small elements get closer to this point and the value therefore rises. In fact, setting up realistic boundary conditions is often the most challenging aspect of a simulation.Ī singularity is a point in the model where a value, such as stress, tends to infinity. Singularities caused by sudden changes in boundary conditions can be harder to spot and resolve. Many singularities are caused by stress-raising geometry such as holes and sharp internal corners, and this is generally well understood. Singularities lead to completely erroneous results and stresses that continue to rise as a mesh is refined. Singularities in Finite Element Analysis (FEA) can cause real issues, even for an apparently simple structural analysis. In fact, setting up realistic boundary conditions is often the most challenging aspect of a simulation. To determine whether results show a real stress concentration or a singularity, an accurate solution can usually be obtained by either using elastic supports or modeling contact between components. But, this can result in singularities that produce erroneous results. FEA boundaries can usually be obtained using simple fixed constraints.