Project (100 points): A notched, rectangular cross-section cantilever beam is loaded in bending (F = 50 lb)

Project (100 points): A notched, rectangular cross-section cantilever beam is loaded in bending
(F = 50 lb). Determine a reasonable finite element mesh and compare its prediction of maximum
stress and deflection with a closed form solution for the points at the beam end (deflection), at
point D (max stress) and at the location of notch (max stress).
The beam dimensions in Figure 1 are: a = 4in, d = 7.5in, 1 = 10in, b = 0.1in, h = lin, and r =
0.167 in. The material is steel (E = 30 x10° psi). The supporting wall is much stiffer than the
beam. At the notch, the stress concentration factor K = 1.56 (for analytical solution). Four
different levels of mesh should be considered. Calculate the maximum deflection and the stress
values at point D and at the notch and compare them with the analytical values through a table.
Plot the mesh convergence for the deflection at the tip. Compare the maximum Von Mises stress
for the entire beam with the theoretical value. Check for the stress singularity and use mesh
metrics to defend the selected mesh.
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(a) Beam geometry
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Figure 1