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

The Beam Element in Large Displacements
Example:
First we need to calculate the nodal coordinates at times t and 0 ( t x 1 , t x 2 ),
( 0 x 1 , 0 x 2 ). Using the corresponding geometries and the following formula:
t x i =
N∑
N t k x k i + t 2
k=1
N∑
k=1
a k N k t V k
ti + s 2
N∑
k=1
where N k are linear shape functions, we obtain:
b k N k t V k
si, i = 1, 2, 3
Institute of Structural Engineering Method of Finite Elements II 43