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### Question Description

I need the project problem solved with the finite element analysis method as shown in the instructions pdf. Please make sure to hit on all the points mentioned in the attached pdf.

Instructions:

1. Submit a “standard” report that includes a cover page (including Course No., Course Name, Project No., name and ID of the student and instructor, date of submission), table of contents, introduction and model description, objectives, methodology including software used, details for both problems (stiffness matrix, force matrix, assembling global stiffness matrix, calculating stress and variation of stress within each element), results (displacement vs. length and stress vs. length) and discussion, and references if any.

2. Figures and tables should have captions and should be referred to in the context.

3. Present your results as graphs rather than printing out data as tables.

4. The graphs must include axis labels with the corresponding units, legends describing the number of elements used.

5. In-class students must provide a hardcopy of the report; while online students should submit their report as a single pdf file in the designated space.

6. Both In-class and online students must email the instructor and the TA a single RAR or ZIP file with the following format for naming the file

Last name_First name_STUDENT ID_Project1.ZIP or

Last name_First name_STUDENT ID_Project1.RAR

This compressed file must include the report and the associated code (separate file and not in the text) and graphs.

7. The acceptance criteria should be clearly identified for selecting the sufficient number of elements.

8. The exact (Analytical) solution of problem is not required but is considered as bonus.

Problem: A bar with variable cross-section is subjected to a uniformly distributed axial load of p =2000 kg/m. The cross-sections at the support, mid-length and free end are 60 x 60 cm^2, 30 x 30 cm^2 and 20 x 20 cm^2, respectively. Assume that the cross-section varies quadratically in between these points on all 4 sides (Hint: Obtain a quadratic formula that passes through the given areas). Assume E=2 x 10^6 kg/cm^2 and L= 5 m.

(a) Determine the displacement along the member using truss elements with 2 nodes (linear interpolation functions). What are the minimum number of elements for convergence? Show the variation of displacement and stress along the member for at least 5 cases.

(b) Determine the displacement along the member using truss elements with 3 nodes (quadratic interpolation functions). What are the minimum number of elements for convergence? Show the variation of displacement and stress along the member for at least 5 cases.

(Hint: For convergence, let the stress distribution be your acceptance criteria).

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