I have a beam subject to twisting and/or bending forces as well as linear compression force along its main axis. It is modelled as an isotropic beam, but if anisotropic is not too far off then that's okay too. The beam is capable of large deformations such that its maximum deformations are:
- 140 degrees in pure bending
- 140 degrees in pure twisting
- 70 degrees bending + 70 degrees twisting
What is an applicable nonlinear beam theory I can apply to this problem using equations rather than any software-based solutions?
I like using the basic undergrad Euler-Bernoulli beam theory, but the assumptions make it invalid in this case and I'm looking for something that is in the same vein as far as calculations goes and does not require significantly more advanced mathematics.
Ideally a theory that reduces the problem to a set of equations that can be solved without requiring multiple pages of tensor calculations that are hard to follow.