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2. Determine the finite element solution to Equation (1) using two unequal length linear elements as follows: u(x) H (1) (2) 2 3 0.75H 0.25H a) Obtain the 3x3 global system of equations for the nodal displacements. Note that the element contributions can be determined by direct analogy with the 1-D model problem. (10 points) b) Incorporate the boundary conditions and solve for the nodal displacements. (5 points) c) Using the original 3x3 system and the nodal displacement values, solve for the reaction force at the point x-0. Verify that the rod is in static equilibrium. (5 points) d) Sketch a plot of the finite element solution for the displacement u(x) over the entire domain, 0≤x≤H. Is your finite element solution an exact solution to Equation (1)? Why or why not? (5 points) e) Using shape functions, calculate the displacement at the mid-point of element 2. (5 points) f) Calculate the stress at the mid-points of element 1 and element 2. Based on these results, what would be the corresponding stress values be at x-0.74999H and x-0.75001H? Do these results pose a problem? If no, explain why not. If yes, how could the problem be remedied? (5 points)