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AERSP_301_HW_7_FEM - AERSP 301 HW#7 Stationary Principle...

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AERSP 301: HW #7 Stationary Principle, Finite Element Method Assigned: Wednesday, October 21, 2009 Due: Wednesday, November 4, 2009 Problem 1 (20 pts) Given the spring system below, use the Stationary Principle of Total Potential Energy to determine the displacements q1, q2, and q3. Leave your answers in terms of spring stiffness and loads. Problem 2 (20 pts): Using at least 2 elements, use the finite element method to analyze the rod shown below. Determine a) The global stiffness matrix and load vector b) The displacements at pts 1, 2, and 3 c) The reaction force at the cantilevered end using the constrained equation E = 10e3 psi , A = 2 in 2 , L = 40 in P1 = 50 lbs, P2 = 100 lbs, f = 5 lbs/in K 1 K 2 K 3 P 4 P 2 P 1 P 3 q 3 q 2 q 1 P 1 P 2 f EA, L 3 x = ¼ L 1 2
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Problem 3 (20 pts): Using at least two finite elements, use the finite element method to analyze the beam shown below. Determine: a) The global stiffness matrix and load vector b) The rotation at the pinned ends c) The deflection at the halfway point E = 10e3 psi, I = 10e4 in
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