Solution of Equilibrium Equations in Static Analysis: LDLT Solution ...

L
LDL T Solution
Recall the Gauss multiplication factors – they enter into L i
‐1
, i = 1, 2, 3:
−1
1
Step 1: Step 2:
r3 = r3 + 8/7 r2;
r4 = r4 + (‐5/14) r2;
r2 = r2 + 4/5 r1;
r3 = r3 + (‐1/5) r1;
r4 = r4;
Step 3:
r4 = r4 + 4/3 r3;
⎡ 1
⎤
⎡1
⎤
⎡1
⎤
⎢
4/5 1
⎥ ⎢
⎢
⎥ 1
0 1
⎥ ⎢
−
= ⎢
⎥
1
0 1
⎥
−
L
⎢ −1/5
0 1 ⎥
2
= L
⎢ 0 8/7 1 ⎥
3
= ⎢
⎥
⎢ 0 0 1 ⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎣ 0 0 0 1
⎦ ⎣
0 − 5/
14
0 1
⎦
⎣
0 0 4/
3
1
⎦
(i.e. the i th column of L i
‐1
contains the multipliers of the i th step)
15-Jun-07
L
⎡ 1
⎤
⎢
4/5 1
⎥
⎢
−
⎥
1/5 −
8/7 1
⎢
⎥
⎣ 0 5/14 −4/3 1⎦
= L1L2L3
= ⎢
⎥
Method of Finite Elements I
14