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

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Assignment#1 (FEM)

Problem#1.25: Suggest a method of finding the stresses in the frame shown in Figure 1.22 using the finite element method.

Now to find equation of “Л” equation (2) and “T” in term of stiffness matrix we will proceed by taking the derivative of equation (1) as follows:

First derivative is,

Second derivative is,

Let us consider that,

Where,

Then,

This can be arranged into matrix form as,

Now,

First term,

Similarly, second term,

Since length of both elements is same that is therefore,

Also global displacement vector,

And global load vector,

Hence since,

Therefore,

Since we have

And there corresponding “P” values are:

We have only “ & “

Hence equation (4) reduces to

This matrix can be written in equation form as follows:

Now the strain can be found as