The Finite Element Method for the Analysis of Non-Linear and ...

The Beam Element in Large Displacements
We need to express the components V k
ti , ZV k
si of the vectors Vk t , V k s in
terms of the nodal rotational degrees of freedom per node k:
θ T k = [ θ k x θ k y θ k z
This in linear analysis would be written as:
V k t = θ k × t V k t
V k s = θ k × t V k s
but in the case of large displacements a second order Taylor approximation
needs to be used:
V k t = θ k × t V k t + 1 2 θ k × (θ k × t V k t )
V k s = θ k × t V k s + 1 2 θ k × (θ k × t V k s)
]
Institute of Structural Engineering Method of Finite Elements II 40