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Problem: A bar with variable cross-section is subjected to a uniform axial load of p =2000 N/m. The cross-sections at the support, mid-length and free end are 60 x 60 cm2, 30 x 30 cm2 and 20x 20 cm2, respectively. Assume that the cross-section varies quathatically in between these point on all 4 sides (Hint: Obtain a quadratic formula that passes through the given areas). Assume E = 2 x 1011 N/m2 and L=10 m.
(a) Determine the displacement at the free end of the bar using Miss element 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 at the free end of the bar using truss element with 3 nodes (quadratic interpolation function;). What are the minimum number of plomont- 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).
The assignment has to be done with matlab programing software or similar (the code is required also) and the result has to be shown graphically Attached you will find the main assignment. To add a little detail to it: The assignment has to be done using matlab or similar programming software. The solution should also be shown graphically. These can be done by dividing the bar into 2, 5, 10, 20, 50 and 100 elements. For convergence can have an acceptable range such as 5-7% or a little more values to justify it.
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