Assignment
FINITE ELEMENT
METHODS
Q.No.4.33. Derive Eqn (4.30) for a cubic triangular element.
Answer:
If a cubic interpolation model is used, 10 nodal unknowns are required. The location of the nodes is
shown in Figure.
The nodes 4 and 5 are located at one-third points along the edge 1-2 with similar locations for the
nodes 6 and 7, and 8 and 9 along the edges 2-3 and 3-1, respectively. The node 10 is located at the
centroid of the triangle 123. In this case, the interpolation model is given by
Where the general form of the nodal interpolation function can be assumed as
For N1 we impose the requirements
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