Single point load introduce stress singularity?

[EricZhao]

Some articles say that never assume single point load or support upon your model, because it will introduce stress singularity. Sounds reasonable. But I remember the FEA will always parse the load or restraint to each node, when the matrix function Kx=F is being built. How to explain this? The load will always appear in the equation with the form of point load.

 

[johnhors]

Eric

You seem to have forgotten the fundamentals of finite element analysis, that is a continuum (the structure you model) is represented by discrete points (the nodes).
Equally a load on any structure is applied as a pressure over a finite area, but this also has to be represented by discrete nodal forces. Thus any pressure loading is applied as an equivalent set of nodal forces. If you manually applied a force at an individual node, it is effectively trying to apply infinite pressure over zero area, and is thus a singularity.

Restraints can also induce singularities, but only under certain circumstances, those being when the model is over constrained or does not have a balanced set of loads applied.

Ideally your model will have balanced loading (all applied as pressures) and a minimal 3-2-1 support set (see previous posts of mine for details).

 

[rb1957]

i've been applying nodal loads for years (decades) without encountering singularities ... i mean why have nodal loads if you can't use them ?

what you will see is very high stresses around the load (because its been idealised to a point), and generally i discount these as being unrealistic.

 

[EricZhao]

Got it,Thanks all

 

[Drej]

> i've been applying nodal loads for years (decades) without encountering singularities

Impossible. As outlined by john above, if you apply a force to a single node, the stress local to that area will be:

Stress = F/A

since the area is effectively zero, the stress is infinite.

> what you will see is very high stresses around the load (because its been idealised to a point), and generally i discount these as being unrealistic

They are most definitely unrealistic. They are theoretically infinite. It is only the mesh density that stops them being shown as infinite. Point loads converge to infinity, as do point constraints and point geometric discontinuities.

There are no problems with point loads -- they are unavoidable in fact; pressure loads for example are converted to nodal loads as described above -- as long as you understand what it is they are doing to your structure/model.