Due to complications I have with drawing and uploading pics at the moment, I'll simply describe the model instead of posting a pic; it's a cantilever beam (ignore the cross section and modulus of elasticity given in the pic, and the force P) of length L = 1, the coordinate axis x is along the beam, and the axis z is pointing downwards, with the origin at the fixed support on the left side of the beam. Imagine some continuous load(adsbygoogle = window.adsbygoogle || []).push({}); qas a function of x distributed along the beam. This is the only load acting on the beam. The modulus of elasticity E and moment of inertia I are assumed to be constant along the beam. One needs to find the displacementwof the beam, i.e. solve the boundary problem:

[tex]EI \frac{d^4 w}{dx^4} = q[/tex] (1)

with boundary conditions

[tex]w(0) = 0[/tex] (vertical displacement at support equals zero)

[tex]w'(0) = 0[/tex] (slope at support equals zero - no rotation)

[tex]EI \frac{d^3 w}{dx^3} = 0[/tex] (shear force at x = 1 equals zero)

[tex]EI \frac{d^2 w}{dx^2} = 0[/tex] (torque at x = 1 equals zero).

This is where I need a push - I assume the first step is to find the variational formulation of the problem? Do I simply have to take some function satisfying the homogenous boundary condition and multiply equation (1) with it, integrate, and try to obtain a variational formulation that way? Further on, I read about the Galerkin approximation method. I'm interested in how exactly to construct the basis functions for the discretization space of the domain [0, 1] of the problem.

Anyone with some experience in FEM modeling of such simple mechanical systems - please help. The book I'm working with isn't specific enough, and it skips some steps. I'd like to solve this problem step by step in a clear and precise manner. Further on, I'm interesting in creating a Mathematica program, i.e. implementing this idea into an algorithm.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# FEM modelling of a cantilever beam

Loading...

Similar Threads - modelling cantilever beam | Date |
---|---|

Modeling of two-phase flows in electric and magnetic fields | Mar 3, 2018 |

Dynamic modeling of a system and transients of the system | Feb 7, 2018 |

Engine Finite Heat Release Model (With Heat Transfer) Help | Feb 5, 2018 |

Aerospace About Model Rocket Design | Jan 28, 2018 |

Q: cantilevered cylindrical shell | Dec 21, 2017 |

**Physics Forums - The Fusion of Science and Community**