Tie constraints in deall.II?

[Alex Cumberworth]

I am considering switching to deal.II for carrying out my elasticity calculations, but I am not sure from the documentation, tutorials, and this user group if it is not too difficult to create a constraint between two surfaces such that they are bonded, or forced to be continuous. In ABAQUS this is called a tie constraint.

Essentially, I would like to solve a problem in which the system has no configuration in which there are no stresses. As a concrete example, consider a beam that is to be pulled into a ring with the ends connected with some other elastic material. The relaxed state of the beam is when it is straight, but in this configuration, the connecting material would be very stressed. If the left and right end of the beam end up with their faces fully in contact, this could be done with displacement boundary conditions. However, it does not seem feasible to use such boundary conditions for other types of connections (i.e., some part of the long edges of the left and right sides of the beams being connected. It seems that the mesh itself needs to be connected.

Any tips, even if very general, would be greatly appreciated, as I can then decide whether it is worth learning how to use the library in detail, or if I should consider other software.

[Wolfgang Bangerth]

> I am considering switching to deal.II for carrying out my elasticity
> calculations, but I am not sure from the documentation, tutorials, and this
> user group if it is not too difficult to create a constraint between two
> surfaces such that they are bonded, or forced to be continuous. In ABAQUS this
> is called a tie constraint

If you can make the mesh at the ends of your object match (e.g., if you want
to bend your object into a ring), then the construction of these constraints
is essentially identical to how one imposes periodic constraints -- namely,
that each degree of freedom one end has to be some kind of linear function of
the corresponding degree of freedom on the other end. deal.II has functions
for this kind of thing that you could base an implementation for your cases on.

If the meshes don't match, e.g., if you want to glue one end piece to the side
of your tube, then the situation becomes more complicated and the usual
approach to this is to use "mortar elements" or (what we used to call) a
master-slave approach where in essence the displacement on one side is
"projected" onto the displacements of the other side. That, too, can be done
in deal.II (and has been done), but it is substantially more complicated
because you have to solve a geometry problem where you ask which point on one
surface a node on the other surface corresponds to.

Best
W.


--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Alex Cumberworth]

Thanks for the information. Unfortunately I am more interested in the second case, so I will look around for examples of the mortar element/master slave approach.

Alex