2. Tapered Rod For a tapered rod (A(x) is not constant), solving the strong form equation is harder, but still possible. For a 1-D rod with fixed end conditions, a constant distributed body force, b(x) = bo = 5 , and a cross-sectional area defined as A(x) = 5+22, the solution for the displaced shape looks like: (a) Determine u(x) if both sides of the rod are fixed (a(0) = 0, u(L) = 0) (b) Given the following: -20, 000ksi, A = 10in, L = 20in, bo-5 , plot your calculated in ' displacement function in MATLAB (c) Now approximate the solution using matrix/direct stiffness methods. Break the rod into several elements of varying areas and lump the distributed forces as point loads at the nodes. Plot your results on the same plot as Part b. (d) Comment on your solution. How does your approximation compare to the exact solution? 2. Tapered Rod For a tapered rod (A(x) is not constant), solving the strong form equation is harder, but still possible. For a 1-D rod with fixed end conditions, a constant distributed body force, b(x) = bo = 5 , and a cross-sectional area defined as A(x) = 5+22, the solution for the displaced shape looks like: (a) Determine u(x) if both sides of the rod are fixed (a(0) = 0, u(L) = 0) (b) Given the following: -20, 000ksi, A = 10in, L = 20in, bo-5 , plot your calculated in ' displacement function in MATLAB (c) Now approximate the solution using matrix/direct stiffness methods. Break the rod into several elements of varying areas and lump the distributed forces as point loads at the nodes. Plot your results on the same plot as Part b. (d) Comment on your solution. How does your approximation compare to the exact solution