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

Simple Bar Example - Revisited
Load step 1: t = 1:
( K + K ) Δ u = R− F − F
0 0 (1) 1 1 (0) 1 (0)
a b a b
⇓
2×
10
Δ u = = 6.6667×
10
7 1 1
10 ( + )
10 5
Iteration 1: ( i = 1)
4
(1) −3
u = u +Δ u = 6.6667×
10
1 (1) 1 (0) (1) −3
1 (1)
1 (1) −4
εa
= = ×
La
1 (1)
b
u
b
6.6667 10 < ε (elastic section!)
1 (1)
u
−3
ε = = 1.3333×
10 < εY
(elastic section!)
L
F
= 6.6667× 10 ; F = 1.3333×
10
1 (1) 3 1 (1) 4
a
b
0 0 (2) 1 1 (1) 1 (1)
( Ka Kb) u R Fa Fb
0
Y
Convergence in one iteration!
1 −3
+ Δ = − − = u = 6.6667×
`10
Institute of Structural Engineering Method of Finite Elements II 30