Low level basis function operations in UFL

variational formulation
1

I would like to model a post-tensioned concrete slab, similar to this paper: (PDF) Layout optimization of post-tensioned cables in concrete slabs

Treating the tensioning cable as a spatial curve (e.g. a Bspline), the shell nodal forces due to the cable {f}_{pe} (three force components, two moments) can be expressed using virtual work. The so-called cable strain matrix B_p (Eq 7) relates the three shell displacements and two rotations to the axial strain of the cable (here shown for one node).

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Here a,b,c are constants (the components of the cable’s normalized tangent vector).

My question is how to best implement something like this B in UFL. The Jacobian components I get via ufl.Jacobian and ufl.JacobianInverse, but I do not remember how to access the basis functions and derivatives. Perhaps there is a more elegant formulation for the nodal forces.

I’m using the linear Naghdi model in fenics-shells as a starting point (@jackhale). Appreciate any suggestions!

2

Hello @niewiarowski. I’m pretty sure I’m too late, but I think for reference it’s worth mentioning that the UFL language is pretty natural. As detailed here, you can access the derivative along the i coordinate of a function f by a simple f.dx(i).

As for basis functions, in the UFL sense of the term these would simple be : ufl.TestFunction(E) and ufl.TrialFunction(E).

3

Hi @hawkspar, thank you for the response. I haven’t looked at this problem in a few weeks, while I have a quasi working solution, it is not ideal. I posted a (hopefully) clearer version of my question here: UPDATED: Constructing nodal force vector involving shape function derivatives - #2 by niewiarowski if you have any advice, thanks again