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

The Beam Element in Large Displacements
This leads to the following formulations
t
u i =
N∑
N kt u k i + t 2
k=1
N∑
k=1
a k N k ( t V k
ti − 0 V k ti) + s 2
N∑
k=1
b k N k ( t V k si − 0 V k
si)
and u i =
where
N∑
N k u k i + t 2
k=1
N∑
k=1
a k N k V k
ti + s 2
N∑
k=1
Vti k = t + ∆ t Vti k − t Vti
k
Vsi k = t + ∆ t Vsi k − t Vsi
k
b k N k V k
si, i = 1, 2, 3
Institute of Structural Engineering Method of Finite Elements II 39