Description:
Computer Homework #1
Starting with the attached Matlab code, develop a program for one- dimensional elasticity. The parts that need to be added are the computational of strain and stress. The program should be able to treat an arbitrary number of elements; the number of elements is specified by the variable, nel, which you must change for different meshes. In the included code, nodes with an essential boundary condition are listed in fixed_nodes. The penalty method is used to enforce the essential boundary conditions.
i. Apply the program to the problem shown below using only 2 elements. Show that the displacement field is linear and that the stress field is constant.
ii. Apply the program to the problem shown below using 2, 4, 8 and 16 elements. Plot the strain and displacement along with the exact solution. Is the natural boundary condition met more accurately as the mesh is refined?
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iii.
Repeat for (c)
iv.
v.
Add a section to your program to plot displacement field, the stress field, and to compute the normalized error in the energy (Chapter 5, pp. 115, eq 5.50). For the problem in (ii) and (iii) plot the log of normalized error in the energy versus the log of the element size. What are the slopes of straight line fits to these curves? Are they what you would expect (see section 5.6.1)?
How many elements are needed to solve (i) exactly? If you wanted to solve (ii) and (iii) exactly using a single element, how many nodes would the element have and why?
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Report:
Computer homework #1 will be submitted in the form of a report. The report should be concise and include at least the following items:
1. Description of the problems being solved.
2. Results presented in a clear and easily understood format.
3. Discussion of the results (what do I see, why do I see the results that I
see, etc.) and the potential implications the results may have for finite element programs.
Please note that marks will be given for spelling, grammar, clarity and style.
Marking Scheme:
50% : Matlab programming and results
30% : Discussion of Results
20% : Clarity, organization and style of the report
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