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

Example
Therefore, we ultimately have:
∂ t x i
∂ 0 x j
=
The nodal coordinates at time t are:
4∑
k=1
( ) ∂Nk t x k
∂ 0 i (5)
x j
( t x 1
1
, t x 1 2) = (2 + 4t, 2) ( t x 2 1, t x 2 2) = (4t, 2)
( t x 3 1, t x 3 2) = (0, 0) ( t x 4 1, t x 4 2) = (2, 0)
(6)
By substituting (4), (5) and (6) into Eqn (2) we obtain:
[ ]
t 1 2t
0X =
0 1
From Lecture 4 we know that the Green-Langrange strain tensor will then be:
t
0ɛ = 1 2 (t 0X T t 0X − I) ⇒
[ ]
t 0 t
0ɛ =
t 2t 2
Institute of Structural Engineering Method of Finite Elements II 13