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).
