Example: Cantilever Beam
The classic introductory FEM example — simulate a cantilever beam and compare with beam theory.
The cantilever beam is the classic introductory FEM example. It has a known analytical solution, which lets you verify your Dr.Q setup is correct before moving on to more complex models.
Goal
Simulate a cantilever beam (fixed at one end, loaded at the free end) and compare the FEM result with the analytical solution from beam theory.
Setup
| Parameter | Value | | --- | --- | | Geometry | Cuboid 200 × 20 × 10 mm | | Material | Steel (E = 210,000 MPa, ν = 0.3) | | Boundary condition | One end face fixed | | Load | 100 N downward at the free end face |
Expected results from beam theory
Maximum tip deflection:
w = FL³ / (3EI) ≈ 0.127 mm
Maximum bending stress at the fixed end:
σ = 6FL / (bh²) ≈ 30 MPa
where F = 100 N, L = 200 mm, b = 20 mm, h = 10 mm.
Comparing with FEM
The FEM result should agree with the analytical solution within 5%. Larger deviations indicate a problem in the setup — wrong material units, load direction, or boundary condition placement.
When FEM and the hand calculation agree, you've confirmed the setup is correct. This confidence is what carries over to more complex models where no analytical solution exists.
Common mistakes in this example
- Force applied as a point load at a single node instead of distributed over the end face (causes a singularity)
- Wrong end fixed (middle face instead of end face)
- Material Young's modulus in GPa instead of MPa → tip deflection 1000× too small