Minimum Bandwidth 2-Finite Element Method-Assignment Solution, Exercises of Mathematical Methods for Numerical Analysis and Optimization

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ASSIGNMENT # 03

[Year]

NUMERICAL PROBLEM

Numerical problem #2.

Statement:

Label the elements and nodes for each of the system shown in figure to produce minimum bandwidth.

Fig 2.

Solution:

The bandwidth is defined as

Bandwidth (B) = (Maximum difference between the numbered degree of freedom at the ends of any member +1) ……………………………… I

This definition can be generalized so as to be applicable for any type of finite element as

Bandwidth (B) = (D+1) .f …………………….. II

Where D is the maximum largest difference in the node numbers occurring for all elements of the assemblage, and f is the number of degrees of freedom at each node.

Node numbering for the system is given below.

Fig: Node numbering

From the above mentioned node numbering, the bandwidth is calculated by using formula II, i.e.

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

Here,

D = Maximum largest difference in node numbers occurring for all elements of assemblage = 12

And

f = Number of degrees of freedom at each node = 3

Therefore,

Bandwidth (B) = (12+1).

Bandwidth (B) = (13).

Bandwidth (B) = 39

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