How to implement Spider Element RBE2 or RBE3

Hi everyone

Spider Element is a popular concept in Structural Dynamics, to

If you have any idea to implement it, please let me know.

Ref:

RBE2 — The active degrees of freedom of the single core node (independent) enforce the active degrees of freedom of the leg nodes (dependent). Therefore, the active degrees of freedom of all nodes included in an RBE2 element are considered rigidly connected.

RBE3 — The weighted average of the active degrees of freedom of the leg nodes (independent) enforces the active degrees of freedom of the single core node (dependent). This weighting is set to 1 and cannot be changed in NX; all nodes contribute to the motion equally. Unlike the RBE2, the RBE3 element is flexible (not infinitely rigid), due to the allowable freedom of the leg nodes. Common uses for this element type include adding and distributing mass without adding stiffness, and distributing a load from multiple points to a single point.

Hello,
this should be possible with the mixed-dimensional branch. The idea being to add the dofs of the master node as additional degrees of freedom using a Real FunctionSpace and enforce the rigid links using Lagrange multipliers living on the corresponding part of the boundary, something like:

a = a_mechanical + dot(lamb, u_ - umaster_)*ds(1) + dot(lamb_, u - umaster)*ds(1)

where u is the displacement field of the continuum, umaster that of the master node and lamb the previously mentioned Lagrange multiplier

When time permits, I plan to add such a demo on the COMET website (https://comet-fenics.readthedocs.io)

Hi Bleyerj

Thank you very much for your reply. When you mentioned ‘mixed-dimensional branch’, were you talking about another version of Fenics, or about using mixed function spaces?

It’s wonderful if you can write a small demo, like 3D square in the picture of a 2D one.

Most of the mixed-dimensional branch should be in master now.