FEATool Multiphysics
v1.10 Finite Element Analysis Toolbox |

Cantilever Beam

A test case for a one dimensional model of a cantilever beam which is fixed to a wall at the left end. Using Euler-Bernoulli beam theory three test cases are studied for which reference solutions are available, a point load at the left end, a uniform distributed load, and the natural vibration modes and frequencies without load.

This model is available as an automated tutorial by selecting **Model Examples and Tutorials...** > **Structural Mechanics** > **Cantilever Beam** from the **File** menu. Or alternatively, follow the step-by-step instructions below.

- To start a new model click the
**New Model**toolbar button, or select*New Model...*from the*File*menu. - Select the
**1D**radio button. - Select the
**Euler-Bernoulli Beam**physics mode from the*Select Physics*drop-down menu. - Press
**OK**to finish the physics mode selection.

First define a line geometry with length *2* and a grid for the simulation.

- Press the
**Create line***Toolbar*button. - Enter
`2`

into the*Line geometry maximum x-coordinate*edit field. - Press
**OK**to finish and close the dialog box. - Switch to
**Grid**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**Refine***Toolbar*button. - Switch to
**Equation**mode by clicking on the corresponding*Mode Toolbar*button. - Enter
`1`

into the*Density*edit field. - Enter
`6`

into the*Cross section area*edit field. - Enter
`3`

into the*Modulus of elasticity*edit field. - Enter
`4`

into the*Cross section moment of intertia*edit field. - Press
**OK**to finish the equation and subdomain settings specification.

Set up the point load on the right boundary.

- Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button. - Select the
**Fixed displacement**radio button. - Select
**2**in the*Boundaries*list box. - Enter
`-5`

into the*Displacement/load*edit field. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**=***Toolbar*button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution.

Verify that the maximum deflection at the end is equal to the analytical solution for a cantilever beam with a point load *PL ^{2}/(3EI) = -1.1111*.

- Select
**Point/Line Evaluation...**from the*Post*menu. - Enter
`2`

into the*Evaluation coordinates in x-direction*edit field. - Press the
**Apply**button. - Press
**OK**to finish and close the dialog box.

Go back to *Equation* mode to define a uniform load, and remove the point boundary condition load.

- Enter
`-5`

into the*Distributed load/force*edit field. - Press
**OK**to finish the equation and subdomain settings specification. - Switch to
**Boundary**mode by clicking on the corresponding*Mode Toolbar*button. - Select
**2**in the*Boundaries*list box. - Enter
`0`

into the*Displacement/load*edit field. - Press
**OK**to finish the boundary condition specification. - Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**=***Toolbar*button to call the solver. After the problem has been solved FEATool will automatically switch to postprocessing mode and plot the computed solution. - Press the
**Plot Options***Toolbar*button.

Verify that the maximum deflection at the end is equal to the analytical solution for a cantilever beam with a uniformly distributed load *q*L ^{4}/(8EI) = -0.8333*.

- Select
**Point/Line Evaluation...**from the*Post*menu. - Enter
`2`

into the*Evaluation coordinates in x-direction*edit field. - Press
**OK**to finish and close the dialog box.

To conduct a eigenmode analysis, change to the corresponding solver in the *Solver Settings* dialog box.

- Switch to
**Solve**mode by clicking on the corresponding*Mode Toolbar*button. - Press the
**Settings***Toolbar*button. - Select
**Eigenvalue**from the*Solution and solver type*drop-down menu. - Press the
**Solve**button.

Verify that the frequencies of the four first vibration modes are close to the reference frequencies *0.198, 1.24, 3.472*, and *6.803 Hz*.

- Press the
**Plot Options***Toolbar*button. - Select
**1.54438 (0.197786 Hz)**from the*Available solutions/eigenvalues (frequencies)*drop-down menu. - Press
**OK**to plot and visualize the selected postprocessing options.

The *cantilever beam* structural mechanics model has now been completed and can be saved as a binary (.fea) model file, or exported as a programmable MATLAB m-script text file, or GUI script (.fes) file.