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The solution to finding the interpolation function of node 1 for a cubic triangular finite element using eq. (el) given in problem 4.7. The steps to calculate the coefficients p1, l(1), and the values of f(l1), f(l2), and f(l3) at nodes 1, 2, and 3 respectively.
Typology: Exercises
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4.11: Using Eq. (El) given in Problem 4.7. Find the interpolation function corresponding to node 1 of a cubic triangular element.
SOLUTION:
m=
R=
N 1 = f(1)(L 1 ) f(1)(L 2 ) f(1)(L 3 )
At node 1 (L 1 =1 L 2 =0 L 3 =0)
So L (1) 1 =1 L (1) 2 =0 L (1) 3 =
For f(L 1 ), P 1 =(3)(1) = 3
So
where
f(1)(L 2 )=1 f(1)(L 3 )=
so
