Effective node numbering scheme

1. Dr. A. S. Sayyad
Professor & Head
Department of Structural Engineering
Sanjivani College of Engineering, Kopargaon 423603.
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
Finite Element Method In Civil
Engineering
Effective Node Numbering
Scheme

2. What is Effective Node Numbering Scheme?
Banded Matrix
A matrix is banded when all elements are zero except those within a band.
1 2 3
4 5 6
7 8 9
1 2 0
4 5 6
0 8 9
1 0 0
0 5 0
0 0 9
The semi-bandwidth/half bandwidth of such matrix is the number of terms within the
band to the right of (including) diagonal.
Effective Node Numbering
Effective Node numbering should be such that semi band width/half band width of the
matrix must be minimum.

3. The semi-bandwidth ‘B’ is given by expression
B = (1+D)f
where,
D = maximum difference in node number in an element after considering
all elements.
f = degree of freedom per node.

4. Example: Let consider a rectangular domain (Rectangular slab) discretized into 4 elements
Solution
Divide the given rectangular slab into 4 elements.
Give the node numbering in sequence following four different ways.
• For Case I and II, move horizontally
• For Case III and IV, move vertically

5. D=
f=
B = (1+D)f
B=
D=
f=
B = (1+D)f
B=
D=
f=
B = (1+D)f
B=
D=
f=
B = (1+D)f
B=

6. Examples: Determine minimum band width of overall stiffness matrix of truss shown in
fig.
Solution:
The node numbers are given in four different ways and then maximum difference between
two consecutive node numbers.