Part VI
Verification
C. Stress recovery · Straight-pipe end forces to stress
A straight pipe 5.0 m long follows global x from node 0 to node 1. Node 1 moves 0.01 m along the pipe and rotates 0.02 rad about its axis. What axial force and torque act at that element end? What axial and torsional shear stresses do these resultants produce?
The case tests transfer from element end forces to stress recovery. Only axial and torsional terms are active.
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 recovers forces from a supplied displacement vector. It does not exercise current admission of imposed boundary motion. The current ordinary preview refuses legacy imposed displacement. Explicit rigid boundary motions belong to the load/reference-state route.
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 |
|---|---|---|
| Elastic modulus | E | 2000.0 Pa |
| Shear modulus | G | 800.0 Pa |
| Area | A | 4.0 m2 |
| Torsion constant | J | 2.0 m4 |
| Torsion radius | r | 0.5 m |
| Length | L | 5.0 m |
| Node 1 axial displacement | ux | 0.01 m |
| Node 1 torsional rotation | θx | 0.02 rad |
2.Method.
Element axial stiffness is EA/L, and torsional stiffness is GJ/L. Multiplication by the imposed stretch or twist gives force or moment at end j. Recovery uses these end values directly, without a sign change.
Axial stress equals end force divided by area. Torsional shear stress equals end torque times torsion radius divided by torsion constant.
3.Results.
| Quantity | Expected |
|---|---|
| End-j axial force, Fx,j | 16.0 N |
| End-j torsional moment, Mx,j | 6.4 N·m |
| Axial normal stress, σaxial | 4.0 Pa |
| Torsional shear stress, τ | 1.6 Pa |
The case record describes these checks:
- The end forces are reported for end j of the element.
- The end axial force matches 16.0 N and the end torsional moment matches 6.4 N·m.
- The axial normal stress matches 4.0 Pa and the torsional shear stress matches 1.6 Pa.
- The stress recovery completes without being blocked.
- The result carries the review flags the program attaches to every result.
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 checked force, moment and stress must match the hand calculation to within an absolute difference of 1.0 × 10−9 in its own units. Yes-or-no conditions, such as the end label and the review flag, are checked exactly. Long values are shown here to seven significant figures; the tests compare the full values in the record.
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 integrated_straight_pipe_resultants_feed_stress_recovery_fixture
Hand calculation:
validation/hand_calcs/stress/integrated_straight_pipe_resultants.md.
Test record, with the recorded run of 2026-07-10:
stress-integrated-straight-pipe-original.md.