Higher-Order Timoshenko Beam Element

[Christopher Wong]

Hello all,

I am going to be developing a new Timoshenko Beam Element that uses cubic-order Hermitian interpolations. The formulation is said to be super-convergent, i.e., it produces an exact analytical solution with a single finite element - much like the conventional Euler-Bernoulli beam element. It is also appropriate for dynamics problems using the same shape functions. The element does not lend itself to shear locking, and thus, requires no special treatment of the primary variables.

There are some particular challenges to this. For starters, how to properly implement the Hermite shape functions on the coupled displacements and rotations. If anyone (*cough* Swetha or Chandu *cough cough*) could chime in on this MOOSE groups thread: https://groups.google.com/g/moose-users/c/NwQbXa75l9U, it would be a huge help!

--Chris

[Swetha Veeraraghavan]

Hi Chris, 

Sorry for the delay in responding. I have replied to your message in the Moose users group, but unfortunately I don't really know a neat way of solving this interpolation problem. 

Regards,

Swetha

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[Chandu Bolisetti]

Hi Chris, 

I don't know much about this either..sorry! 

Chandu

[Christopher Wong]

Thanks guys. Looks like this is a novel problem that I will just have to find a new technique on my own to be able to solve.

--CJW