Consider a beam, modelled with “Euler–Bernoulli Beam” finite elements.
The beam is initially deformed with the set of forces "F" and torues "M", applied at the nodes, shown in Figure.
[Direction of the forces and torues are as per the blue and red arrows, correspondingly, and also explicitly expressed with the signs of "F" and "M", assigned as per the sign convention in the FEM Chapter by P.M.Trivailo]
All these forces and torques are instantaneously removed at t=0, allowing the beam to vibrate freely.
Use FEM, programmed in MATLAB, to calculate displacement of the Node #12 at t=0.1 s.
[It is acceptable if your answer deviates from the presented option within ±2 mm tolerance (i.e.is within plus/minus 2 mm band)].
In addition to the information, shown in the Figure, use the following data:
? Total length of the beam, L: 2.8 [m];
? Cross section of the beam (width x high): 60 [mm] x 8 [mm];
? Young Modulus E: 200*10^9 N/m^2 [Pa];
? Density of the material of the beam, ?: 7500 [kg/m^3];
? Assume zero damping;
? Number of Finite Elements: 14;
? Length of each Finite Element: 0.2 [m];
? List of pinned nodes: [4,9,15];
? Use the following time step: 0.0002 [s].