Part VI
Verification
C. Stress recovery · Thin-wall pressure membrane stress
A thin cylindrical wall of radius 3.0 m and thickness 0.5 m holds internal pressure of 100.0 Pa. What hoop and longitudinal membrane stresses follow? Pressure, radius and thickness enter directly. Recovery does not derive these inputs from a pipe size.
This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.
These calculations recover separate stress components, not code stress. The current ordinary preview reports supported straight circular normal-stress extrema. Torsional shear remains separate, and arc maxima are withheld. Component recovery in this benchmark does not establish the current maximum or its coverage.
This benchmark supplies pressure inputs directly to the historical membrane-stress helper. The current ordinary preview refuses nonzero legacy pressure. The exact_straight_pressure_v2 route admits homogeneous isotropic straight circular members. It requires selected E/nu, explicit collinear equal-bore pressure regions, terminal ownership and declared closure-transfer paths. Pressure is uniform internal differential pressure with zero external pressure. This recorded calculation does not establish that route.
The formulas use the mean radius of a thin wall; code forms such as pDo/4t differ slightly. This component comparison does not establish a current pressure solve. The exact_straight_pressure_v2 path requires straight circular pipe, explicit pressure regions and terminal ownership, E/nu, and declared pressure-reference assumptions. Fresh solves refuse nonzero legacy pressure (Status).
1.Inputs.
Illustrative values, taken from no standard and chosen so the arithmetic can be followed by hand. Most do not describe a real pipe; read them in any consistent set of units.
| Quantity | Symbol | Value |
|---|---|---|
| Pressure | p | 100.0 Pa |
| Membrane radius | r | 3.0 m |
| Wall thickness | t | 0.5 m |
2.Method.
The thin-wall membrane results are used. The hoop stress balances the pressure across a cut along the axis and equals pr/t. The longitudinal stress balances the pressure on a closed end against the wall ring and is half the hoop stress.
3.Results.
| Quantity | Expected |
|---|---|
| Hoop membrane stress, σhoop | 600.0 Pa |
| Longitudinal membrane stress, σlong | 300.0 Pa |
The case record describes these checks:
- The stress recovery completes without being blocked.
- The hoop stress matches 600.0 Pa.
- The longitudinal stress matches 300.0 Pa.
What it shows. Compared with an independent hand calculation.
Path exercised. The benchmark calls the solver’s components directly: elements, loads, frame solver and stress recovery. It does not go through the program’s own model-to-solve path.
Agreement. Each recovered stress must match the hand calculation to within an absolute difference of 1.0 × 10−9 Pa. Yes-or-no conditions, such as whether the result is blocked, are checked exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.
Why is longitudinal stress exactly half the hoop stress? Cut the cylinder along its axis. Per unit length, pressure acts on projected width 2r, resisted by two wall sections of thickness t. Cut the cylinder across its axis. Pressure acts on end area πr2, resisted by ring area 2πrt. The first balance gives pr/t, and the second gives pr/2t.
4.Recorded command.
This command belongs to the linked case record and its recorded execution path. This website update did not rerun it. A historical command or result does not establish current product support.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/stress/Cargo.toml recovers_pressure_membrane_fixture
Hand calculation:
validation/hand_calcs/stress/pressure_membrane.md.
Test record, with the recorded run of 2026-07-10:
stress-pressure-membrane-original.md.