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Your turn ~7 min · ~55 min remaining

Your first check

Confirm files, deformation direction, and order of magnitude right after running.

Your first check

Immediately after running, perform these four checks:

  1. The solver finished without a fatal error.
  2. The file m00_cantilever.rst exists.
  3. The free end moves toward −Y.
  4. Displacement is on the order of tenths of a millimetre, not metres or microns.

Displacement reference

For a rectangular beam with Euler–Bernoulli theory:

I = B·H³/12
|uy_tip| = P·L³/(3·E·I) ≈ 3.81E-4 m ≈ 0.381 mm

You do not need to memorize 0.381 mm. Use it as order-of-magnitude guidance. The template runs PLNSOL,U,SUM in /POST1 right after SOLVE; compare your prediction with the contour produced by the script.

MAPDL total displacement contour PLNSOL U SUM
Figure 5. Total displacement contour from the script (PLNSOL,U,SUM). Compare −Y direction and order of magnitude with the analytical prediction.

Check your model: contrast prediction and contour; do not memorize the decimal. The 3D solid model does not have to match Euler–Bernoulli exactly; M04 and M07 will turn this comparison into a formal study.

Stress reference with Navier

Just as we predicted deflection, we can estimate bending stress with the Navier flexure equation. At the fixed support (x = 0) bending moment is maximum: 

M_max = P·L
σ_ref = M_max·y/I     with y = H/2
σ_ref ≈ 12 MPa

Substituting model values (P = 1000 N, L = 1 m, H = 0.10 m, I = 4.1667E-6 m⁴) gives σ_ref ≈ 12.0 MPa. Under dominant bending, the von Mises equivalent stress plotted by PLNSOL,S,EQV should be compared by order of magnitude against σ_ref. The peak usually appears near the fixed support, not at the loaded tip.

von Mises equivalent stress contour PLNSOL S EQV
Figure 6. von Mises equivalent stress from the script (PLNSOL,S,EQV). Compare peak order of magnitude with σ_ref.

Engineering insight: a meshed 3D solid does not reproduce the Navier–Euler beam exactly. M01 will turn uy_ref and sigma_ref into verifiable parameters; M07 will formalize the FE/analytical comparison.

MAPDL practice

Practice: change the height and validate your results

Change H to 0.12 m in your template, predict before running, and compare theory with the maxima shown by MAPDL.

Execution cycle

  1. 1 In your copy of 00_session_template.mac, change only the height to H = 0.12 m; keep the rest of the contract.
  2. 2 Calculate theoretical |u|max and Navier σmax before running.
  3. 3 Run your modified script and confirm there is no fatal error and the .rst exists.
  4. 4 Read PLNSOL,U,SUM and PLNSOL,S,EQV; enter all four values with units in the form.

Calculate the two analytical cantilever values (H = 0.12 m) before running MAPDL. Tolerance ±1 %.

mm
MPa

Run the practice .mac, read the PLNSOL maxima, and enter displacement in mm and von Mises in MPa.

mm
MPa

Graduated hints

1 · Separate magnitudes

Navier nominal σ is not comparable with the global von Mises peak near the fixed end.

2 · Commands

After SET,LAST use PLNSOL,U,SUM and PLNSOL,S,EQV; record the global maximum shown by each contour.

3 · Criterion

Check units, tolerance, and that deflection drops when H increases; the SEQV peak should be the same order of magnitude as Navier nominal σ (~8 MPa).

Download m00-kit.zip