Question 8.1: Finite Element Analysis of a Notched Cantilever Beam Problem...
Finite Element Analysis of a Notched Cantilever Beam
Problem: A notched, rectangular cross-section cantilever beam is loaded in bending by a fully-reversed transverse force. Determine a reasonable finite element mesh and compare its prediction of maximum stress and deflection with a closed form solution for points at the beam end l, distance b, and the notch at a.
Given: The beam dimensions in Figure 8-7a are: a = 4, d = 7.5, l = 10, b = 0.1, h = 1, and r = 0.167 in. The load F = 25 lb. The material is steel.
Assumptions: The supporting wall is considered to be much stiffer than the beam. Beam weight is negligible compared to the applied load. The reduction in beam cross section due to the notch has a minimal effect on the total beam deflection, but a significant effect on the local stress. A 2-D FEA model is sufficient as plane stress may be assumed.
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