FEATool Multiphysics
v1.17.0
Finite Element Analysis Toolbox

A test case for a one dimensional model of a cantilever beam which is fixed to a wall at the left end. Using EulerBernoulli 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 stepbystep instructions below.
First define a line geometry with length 2 and a grid for the simulation.
2
into the Line geometry maximum xcoordinate edit field.1
into the Density edit field.6
into the Cross section area edit field.3
into the Modulus of elasticity edit field.4
into the Cross section moment of intertia edit field.Set up the point load on the right boundary.
5
into the Displacement/load edit field.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.
2
into the Evaluation coordinates in xdirection edit field.Go back to Equation mode to define a uniform load, and remove the point boundary condition load.
5
into the Distributed load/force edit field.0
into the Displacement/load edit field.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.
2
into the Evaluation coordinates in xdirection edit field.To conduct a eigenmode analysis, change to the corresponding solver in the Solver Settings dialog box.
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.
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 mscript text file (available as the example ex_euler_beam1 script file), or GUI script (.fes) file.