Stress Recovery Explorer

Your tasks

1. 4-node 2 × 2 mesh, probe (3.5, 1.3): the lecture point (Plane Stress Part 3, Activity 1). Compare with your hand calculation.
   Check answer

   σ_xx = 315, σ_yy = −45, σ_xy = −311 kN/m²; σ₁ = 494, σ₂ = −224; von Mises 637. By hand you need the displacements to five decimals: ε_yy is the difference of v₆ = −0.13042 and v₉ = −0.13058, and rounding them to three decimals doubles it.

2. Keep the point and refine: 8-node 16 × 8, then 32 × 16. Does σ_xx approach beam theory’s 225 kN/m²? Then probe mid-span, (2.0, 1.3).
   Check answer

   No. It settles near 150 kN/m², because 0.5 m from the loaded edge the uniform end traction is not the parabolic shear that beam theory assumes (St-Venant). At mid-span the FE gives 900 kN/m², equal to beam theory. Check against beam theory only away from the ends.

3. Run the corner study. Does the peak σ_xx next to the fixed corner converge?
   Check answer

   No: 4 134 → 5 372 → 6 400 → 7 467 kN/m² as the elements shrink, and it passes the beam value. A re-entrant corner of a fully fixed edge is a stress singularity of the elastic model; do not report that peak.

4. On the 4-node 4 × 2 mesh compare Elemental mean, Unaveraged and Averaged. Where do neighbouring elements disagree most?
   Check answer

   Near the fixed edge, especially at its corners, and wherever the stress changes fastest. The jumps shrink as you refine: their size is a free indicator of the mesh error. ANSYS shows the same three options.