Finding Interpolation Function for Node 5 of a Cubic Tetrahedron Element in FEM, Exercises of Mathematical Methods for Numerical Analysis and Optimization

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Assignment Chapter#

Finite Element Method

Problem # 4.

Problem#4.15 Using Equation (E1) given in problem 4.12, find the interpolation function corresponding to node 5 of a cubic tetrahedron element.

Where

And

Solution

A cubic tetrahedron element is shown as follows

For cubic tetrahedron element we have in equation (E1)

Similarly for we have

As

So

Similarly for we have

As

So we have from equation (E1)

Similarly for we have

As

So we have from equation (E1)

Now inserting values of in equation (1)

We will get