For the example, we create a model of a cantilever (steel S235, isotropic, linear elastic) with a T-shaped cross-section and a linearly variable cross-section height.
The geometric data of the component are as follows:
| Cantilever length l | 2800 | mm |
| Cross-section height h0 | 800 | mm |
| Cross-section height hl | 200 | mm |
| Flange width b | 200 | mm |
| Flange thickness tf | 20 | mm |
| Web thickness tw | 10 | mm |
The support conditions and loads are assigned:
- Rigid restraint of the flange and web (translational and rotational) on the restrained side
- Fixation transverse to the longitudinal axis (translational in the Y-direction) at the free end
- Loading with a constant line load of 1.0 kN/m
The Structure Stability add-on is activated for the load case and set with the following parameters:
| Type of Stability Analysis | Eigenvalue method (linear) |
| Number of lowest eigenvalues | 3 |
| Eigenvalue Method | Lanczos |
To mesh the model, the following mesh settings are required:
| Target length of finite elements | 40 mm |
| Independent mesh preferred | Yes |
For an overview of the boundary conditions of the modeling, please click the following image:
After the calculation, the "Stability Analysis" category is selected in the Results Navigator or in the tables. For the first, the smallest eigenvalue, a critical load factor f of 41.427 is obtained. This is used to calculate the critical load:
qcr = 1.0 kN/m ⋅ f ≃ 41.4 kN/m
The corresponding failure mode is displayed as follows:
Excursus: Modeling Cantilever as Member
« Why do we model a cantilever using surface elements; wouldn't it be easier to use a member? »
To answer this question, we create a new model and model the cantilever as a member with the boundary conditions mentioned above; we only adjust the size of the finite elements: Over the length l = 2800 mm, we would like to create 20 finite elements. To do this, we edit the mesh settings or assign a line mesh refinement (target FE length LFE = 140 mm).
Boundary conditions are shown in the image:
The stability analysis results speak for themselves: the large critical load factor f of ≃ 77,323 and the failure modes do not represent the local buckling behavior of the cantilever close to reality.
However, the modeling of the cantilever as a member is sufficiently accurate for calculating the equilibrium conditions (structural analysis): the maximum displacement at the free end of the cantilever is 0.1 mm for both models.