Assignment#03
Finite Element Methods
Problem 3.5
Statement:
Show that the condition to be satisfied for constant value of the field variable is
, where denotes the shape function corresponding to node i and r represents the
number of nodes in the element.
Solution
We know that the shape function represents the order of the interpolation model chosen for the
variation of the field variables.
If the field variable is represented by the linear model
Φ(x) = α1 + α2x
Then N1(x) =1-x/ℓ
N2(x) =x/ℓ
So shape functions are also linear.
If we choose quadratic interpolation model
Φ(x) = α1 + α2x+ α3x2
The shape function is also quadratic .therefore if the field variable is constant then shape
functions are also quadratic.
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