Topic #1: Rayleigh-Ritz Method (RRM) Problem 1 a) Find the exact solution for the beam torsion...

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Topic #1: Rayleigh-Ritz Method (RRM) Problem 1 a) Find the exact solution for the beam torsion problem shown above. The loading consists of a uniformly distributed torque m and a point torque M applied at the end (x=L). The beam is fixed at x=0. b) Two of the following four basis functions are admissible. Indicate which ones and why. Use the RRM with a 2-term expansion using these two basis functions to solve the beam torsion problem. sin (Ix/L) cos (Ix/L) mo (Nm/m) M=2moL , J, L sin (21x/L) cos (21x/L) c) Compare graphically the solutions found in a) and b) and comment on your solution. d) Writing the approximate solution as n (x) = ai fi(x), i=1 obtain the general expression of the linear system [K] {q} = {Q} for this problem, where {q} denotes the vector with the unknown coefficients qi. Topic #1: Rayleigh-Ritz Method (RRM) Problem 1 a) Find the exact solution for the beam torsion problem shown above. The loading consists of a uniformly distributed torque m and a point torque M applied at the end (x=L). The beam is fixed at x=0. b) Two of the following four basis functions are admissible. Indicate which ones and why. Use the RRM with a 2-term expansion using these two basis functions to solve the beam torsion problem. sin (Ix/L) cos (Ix/L) mo (Nm/m) M=2moL , J, L sin (21x/L) cos (21x/L) c) Compare graphically the solutions found in a) and b) and comment on your solution. d) Writing the approximate solution as n (x) = ai fi(x), i=1 obtain the general expression of the linear system [K] {q} = {Q} for this problem, where {q} denotes the vector with the unknown coefficients qi.