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

Setting up the governing equations
From the last Lecture we obtained the Total Lagrangian (TL)
Formulation of the principle of Virtual Displacements:
∫
t+∆t
0 S ij δt+∆t 0 ɛ ij d 0 V = t+∆t R (1)
0 V
where the Green-Lagrange strain component has been defined as:
(
)
t+∆t
0 ɛ ij = 1 3∑
t+∆t
0
2
u i,j + t+∆t
0 u t+∆t
j,i + 0 u k,i t+∆t
0 u k,j
If we denote 0 ɛ ij , 0 u i as increments in the strains and displacements
respectively we can write:
k=1
δ t+∆t
0 ɛ ij = δ t 0ɛ ij + 0 ɛ ij (2)
Institute of Structural Engineering Method of Finite Elements II 2