Problem 3 (40 points): Solve for the axial displacement distribution in the tapered bar shown below. For the finite element discretization, use 3, 5, 7 elements. Evaluate the area at the center of each element length and use that area for each element.
Let A0 = 2 in2, L = 30 in., E = 10^6 psi and P = 1500 lb.
(a) (20 points): Plot the analytical solution and these three results all in one graph. The graph should include: title, labels for the x and y axis and legend. Use different colors for each line.
Analytical solution is: u(x) = (PL / (A0*E)) * ln((L + x) / 2L)