Stress and Fracture Analysis of a Gravitating Cantilever Beam

This research article presents stress distribution and fracture analysis of a cantilever beam considering both continuum and lumped distribution of gravity force. Airy stress function is used to derive two-dimensional stress distribution using power series and boundary conditions. It is concluded that bending stress is the most dominant over other two stresses. However, variation of vertical normal stress does not match between the two systems owing to change in load distribution. Moreover, an expression for energy release rate is also derived by assuming that a crack is present at the top of fixed end of beam and propagates vertically down to result in catastrophic failure. Finally, these results are validated with finite element simulations as well.