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Interpolation Function-Finite Element Method-Assignment Solution, Exercises of Mathematical Methods for Numerical Analysis and Optimization

Aligarh Muslim UniversityMathematical Methods for Numerical Analysis and Optimization

This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Interpolation, Function, Corresponding, Node, Quadratic, Triangular, Element, Order, Model

Typology: Exercises

2011/2012

Uploaded on 07/08/2012

ramu
ramu 🇮🇳

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ASSIGNMENT # 04
PROBLEM # 4-10
4-10 Using Eq (E1) given in problem 4.7, find the interpolation function
corresponding to node 4 of a quadratic triangular element.
Ni = f(i) (L1) f(i) (L2) f(I) (L3) -----------------E1
Where
………………. E2
i = 1, 2, 3, --------- n number of node
m = order of interpolation model
Solution
Here m = 2, i = 4
At node 4 L1 = , L2 = , L3 = 0
for f(4) (L1) 1
so k = 1 to 1 Put these value in equation E2
1
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ASSIGNMENT # 04

PROBLEM # 4-

4-10 Using Eq (E1) given in problem 4.7, find the interpolation function corresponding to node 4 of a quadratic triangular element.

Ni = f(i)^ (L 1 ) f(i)^ (L 2 ) f(I)^ (L 3 ) -----------------E

Where

………………. E

i = 1, 2, 3, --------- n number of node

m = order of interpolation model

Solution

Here m = 2, i = 4

At node 4 L 1 = , L 2 = , L 3 = 0

for f(4)^ (L 1 ) (^1)

so k = 1 to 1 Put these value in equation E

1

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So f(4)^ (L 1 ) = (2L 1 -1+1)

f(4)^ (L 1 ) = 2L 1 ----------------- (1)

for f(4)^ (L 2 ) (^2)

so k = 1 to 1 Put these value in equation E

So f(4)^ (L 2 ) = (2L 2 -1+1)

f (4)^ (L 2 ) = 2L 2 ------------------- (2)

For f (4)^ (L 3 ) 3 = 2 × 0 = 0

From Eq (E2) f(4)^ (L 3 ) = 1 ------------------(3)

Put Eq (1), (2) and (3) in Eq (E1)

N 4 = (2L 1 ) (2L 2 ) (1)

So the final answer is N 4 = 4L 1 L 2

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