Impose displacement on only one node of the FEM mesh

[slll]

Hi experts,

I am experimenting with a FEM package and try to solve a very simple static linear problem :
Take a sphere made up of solid linear isotropic elastic material. Impose :
- zero displacement on the boundary of the sphere and
- arbitrary displacement to the node located at the center of the sphere (the mesh was generated to ensure there is one node there).
In order to minimize the energy of deformation, I would expect that the displacement imposed at the sphere centre would be smoothly damped to zero at the boundary of the sphere.
Instead of that I observe that the displacement is abruptly damped on the first couple of cells surrounding the center point, whatever the mesh refinement. This leads to inverted mesh.
I have the feeling the solver used is not robust enough to deal with such one-point constraint. Any idea or suggestions for improvement ?

Thanks
Sylvain

 

[johnhors]

Do the published NAFEMS tests instead, applying displacements on one node for continuum elements does not make sense.

http://www.Roshaz.com

 

[slll]

Actually the idea is not to simulate something real but to use linear elasticity in order to perform interpolation between known displacements vector of a cloud of points. The cloud of points are considered part of an elastic continuum, supposed to deform under the effect of their imposed displacements.

It seems to me that the problem is well posed even though the situation would be difficult to experiment. Maybe you can imagine of piece of rubber molded around a small magnet that you put in a strong magnetic field, while holding the surface.

 

[johnhors]

Applying a point load at a node or imposing an enforced displacement at a single node creates a stress singularity.

You cannot expect any FE software to give you meaningful results.

You could perhaps create a small spherical void at the centre and apply a pressure to the void surface. Be sure to put sufficient elements on the void surface.

http://www.Roshaz.com

 

[slll]

Ok thanks,
I also see that using an elastic-plastic material can also help going around the problem. I'll see if I can improve that, or if the whole thing is just a bad idea.

 

[ESPcomposites]

I think the second half of the second sentence makes more sense than the rest.

Brian

http://www.espcomposites.com

 

[rb1957]

"zero displacement on the boundary of the sphere" ... does this mean that the sphere is rigidly supported over it's surface ? ie each surface node can react x,y, z loads and won't displace.

if it is, then the nodes adjacent to the displacement will react the load, and most of the sphere will be doing nothing.