tests: add the NAFEMS LE5 Z-section oracle case

The Z-section cantilever under an end torque as five hex20 blocks (two
flanges, two corner blocks, the web; two elements through every wall):
axial stress at A, on the mid-surface of the lower flange at its free
edge, -109.45 against -108 (2%).

The solid model converges to about -109.7, 1.6% beyond the thin-walled
reference, as ESRD's converged p-version solid (-109.5) does. The README
also records the MITC4 mid-surface shell model of the same problem,
which converges to about -111.3 (3.1%), and why the case is the solid.

Part of #97.
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Christian Svensson authored and Irakli Kourtis committed 2026-10-18 08:31:48 -04:00
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{
"title": "NAFEMS LE5 Z-section cantilever (hex20)",
"kind": "benchmark",
"source": "NAFEMS, The Standard NAFEMS Benchmarks, TNSB Rev. 3, October 1990, test LE5 (target: axial stress −108 MPa at A, mid-surface); the problem and target as reproduced in the Abaqus 2016 Benchmarks Guide, section 4.2.5 'LE5: Z-section cantilever', and in the ESRD StressCheck Benchmarks Guide 'The Standard NAFEMS Benchmarks: Linear Elastic Tests' (2018), p. 15",
"quantities": [
{
"id": "sxx_A",
"quantity": "σ_xx at A (2.5, −1, −1), mid-surface of the lower flange at its free edge",
"measure": {"command": "solve.probe", "params": {"step": "Torque", "at": [[2.5, -1, -1]]}, "pointer": "/nodes/0/stress/0"},
"value": -108.0,
"tolerance": {"relative": 0.02},
"reason": "the target is published to three figures and comes from a thin-walled idealisation; a 3D solid model of the section converges about 1.5% beyond it (ours: −109.46 here, −109.60 on the next mesh; ESRD's p-version solid: −109.5, see README)"
}
]
}