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

Practical issues (1)
LDL T Solution
• Simultaneous computation of V and L ‐1
i .
• L and V not computed from scratch, but by modifications of K
and R.
• K is symmetric, banded and dpositive‐definite; ite the two oformer
properties permit the compact storage in a 1‐D Array,
complemented by a 1‐D address array:
K
⎡ 5 −4 1 0 ⎤
⎢
−
−
⎥
4 6 4 1
= ⎢
⎥
⎢ 1 − 4 6 − 4 ⎥
⎢
⎥
⎣ 0 1 −4 5 ⎦
a = [ 5 6 − 4 6 − 4 1 5 − 4 1]
non‐zero elements of upper half and diagonal
b = [1 2 4 7]
array indices of the diagonal elements in a
15-Jun-07
Method of Finite Elements I
16