Four node beam element

Hello,

As part of a university assignement I have to develop a four node beam element capable to account for shear deformation and thermal loads. I have to perform static plus natural vibration modes analysis.

I am not experienced on developing elements from a scratch, and I need some hints refering:

1) Interpolation functions: I am planning to use Hermitian Polynomials. I found a very helpful paper of Charles E. Augard to derive them from Lagrange Polynomials. I couldn't find another way to derive interpolation functions for this four node C1 element. What do you think about this?

2) Beam theory. I know there are many theories accounting for shear deformation, but I dont know where to study them from (I am interested in the simplest one tough). Is the stiffness contribution due to shear included only in rotational dof?

3) Are there any software using such an element? I couldn't find any, I think this element is useful only for learning purposes.

I am using two books: one from Cook, Malkus and Plesha (Concepts and applications of FEA) and other from Huebner, Thornton and Byron (The FEM for engineers). Please tell me If you think I am on the right path.

Any other information regarding these topics may be helpul.

Thanks!

Federico Bertoli
Universidad Tecnológica Nacional
Buenos Aires, Argentina