Part VI
Verification
A. System benchmarks · A separately supported pressure closure
An L line has an anchor at A and a free end at D. A realized circular bend joins two straight pipes.
Internal pressure is 5.0e6 Pa. The closure at A is separately supported or compensated. The closure at D transfers its cap load to the wall.
The independent reference uses the direct unit-load method. The current test calls the captured product API in both solver modes and document versions.
This case compares independent numerical values. It does not exercise desktop authoring, the native CLI or report export.
The reference matches small-strain linear elasticity with homogeneous isotropic material and a user-entered bend flexibility factor.
The formulation excludes flow momentum, transient loads, Bourdon bend opening, pressure stiffening and ovalization.
The frozen expectations predate this refresh. The date below records a new product comparison, not a new reference derivation.
The focused test passed on 2026-10-12: one test passed, none failed. Its assertions cover 316 reference, mode and document-version configurations.
1.Inputs.
The table gives the declared reference inputs. Units are stated for each quantity.
| Quantity | Symbol | Value |
|---|---|---|
| Node A coordinates | A | (0.0, 0.0, 0.0) m |
| Node B coordinates | B | (3.0, 0.0, 0.0) m |
| Node C coordinates | C | (3.25, 0.25, 0.0) m |
| Node D coordinates | D | (3.25, 4.25, 0.0) m |
| Bend radius | R | 0.25 m |
| Bend flexibility factor | k | 1 |
| Outside diameter | OD | 0.1683 m |
| Nominal wall | t | 0.00711 m |
| Mill tolerance | m | 0.000889 m |
| Elastic modulus | E | 2.0e11 Pa |
| Poisson ratio | nu | 0.3 |
| Internal pressure | p | 5.0e6 Pa |
| Support | A | Anchor; all six freedoms restrained |
| Terminal A closure transfer | A | separately_supported_or_compensated |
| Terminal D closure transfer | D | transfers_to_wall |
2.Method.
The reference integrates axial, torsional and bending flexibility over the whole line. It does not use a curved-element stiffness matrix.
Pressure caps produce wall tension. The pressure eigenstrain includes Poisson contraction on each straight and arc.
Positive wall force means tension. The effective axial force is wall force minus pressure times bore area.
The reference uses meters and pascals. The product converts translations to millimeters and bending or torsion stresses to megapascals. Axial membrane stress stays in pascals.
The closure at A still carries the outward pressure cap force. Its separate support supplies the opposite force.
No cap force transfers from closure A into the pipe. The pipe anchor reaction changes, although node movement and wall tension match the transferring-cap case.
3.Results.
| Quantity | Expected |
|---|---|
| Closure A outward cap force X | -9.539335e+4 N |
| Closure A transfer to pipe X | 0 N |
| Closure A separate support reaction X | 9.539335e+4 N |
| Pipe anchor A reaction X | -9.539335e+4 N |
| Node D displacement X | 1.957468e-4 m |
| Node D displacement Y | 2.559766e-4 m |
| Bend wall axial force at midspan | 9.539335e+4 N |
| Bend effective axial force at midspan | 0 N |
The case record describes these checks:
- The test compares every valued reference case in both sparse_interactive and dense_scrutiny modes. Each document runs as 0.3.0 and 0.4.0.
- The comparisons include node movement, support reactions, station forces and stresses, end actions and terminal cap transfers.
- The test requires the pressure integrity verdict and checks required row absences on arcs.
- The wall end action follows the end tangent. The arc elastic end-force rows use the chord frame. These quantities have different meanings.
What it shows. Compared with an independent reference calculation.
Path exercised. The captured product API, in both solver modes and both document versions. The comparison does not exercise desktop authoring, the native CLI or report export.
Agreement. The test requires |observed − expected| ≤ 1e-9 × max(|expected|, zero_scale(group)). The frozen reference defines each group floor. Exact unit conversion precedes comparison. Long values are shown here to seven significant figures; the tests compare the full values in the record.
Closure support and pipe support are different actors. The separate closure support balances its cap; the pipe anchor balances the remaining pipe loads.
4.Recorded command.
This command ran against source a72f994d89d901b185116e6565bacb201b69e151 on 2026-10-12. The linked execution record states the result and its scope.
git checkout --detach a72f994d89d901b185116e6565bacb201b69e151 cd projects/chirality-piping cargo test --offline --locked --manifest-path core/product_physics/Cargo.toml --test t4_u2_pressure_references i7_valued_cases_match_in_both_modes_and_document_versions -- --exact
Execution record: 2026-10-12.
Reference calculation:
validation/references/t4_i7/u2_reference_cases.json.
Test source for the execution of 2026-10-12:
t4_u2_pressure_references.rs.