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

The Beam Element in Large Displacements
The finite element equations in this case are:
t K
⎡
⎢
⎣
.
u k
θ k
.
⎤
⎥
⎦ = t + ∆t R − t F (1)
Having solved Eqn (1) for bfu k , θ k , we obtain the approximations for the
nodal point displacement and direction vectors:
t + ∆t u k = t u k + u
∫ k
t + ∆t V k t = t Vt k + dθ k × τ Vt
k
V
∫ k
t + ∆t V k s = t Vs k + dθ k × τ Vs
k
V k
The above formulation corresponds to an iteration of the Newton-Raphson
method
Institute of Structural Engineering Method of Finite Elements II 41