Part VI
Verification
E. Algorithm and software checks · Rotation release, then gap closure
A single frame member is fixed at its root. Its tip carries a transverse force of 1.0 N. The tip’s rotation about z is held by a lift-off support that starts in contact, and a transverse gap of 0.002 mm, initially open, stands beside the tip in y. One support’s change may alter what the other sees. Does the solver follow such a chain one step at a time, and where does it settle?
The one-way support on a rotation is a numerical test of the iteration on a rotational degree of freedom. No such device exists in piping.
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 |
|---|---|---|
| Tip transverse force | Fy | 1.0 N |
| Lift-off support | — | Rz at the tip |
| Gap support | — | Uy at the tip |
| Gap clearance | c | 0.002 mm |
| Initial lift-off state | — | active (in contact) |
| Initial gap state | — | inactive (open) |
2.Method.
On the first iteration only the rotational lift-off support changes: it releases. With the tip now free to rotate, the second iteration changes the classification of the gap, which closes. On the third iteration neither support changes, so the loop has converged. The changed-support counts run 1, 1, 0.
The reference for this group records the expected support states, changed-support counts and final residuals. It does not work out displacements or reactions, so none are tabulated here.
3.Results.
| Quantity | Expected |
|---|---|
| Changed supports, iteration 1 | 1 (Rz lift-off) |
| Changed supports, iteration 2 | 1 (Uy gap) |
| Final changed-support count | 0 |
| Iteration count | 3 |
| Free-DOF force residual | 0.0 N |
| Free-DOF moment residual | 0.0 N·mm |
| Final free-DOF work residual | 0.0 N·mm |
| Final lift-off state | inactive (released) |
| Final gap state | active (closed) |
| Converged | true |
| Diagnostic | none |
The tests check that:
- The solve converges in exactly 3 iterations, with changed-support counts of 1, 1 and 0 in that order.
- The first iteration changes only the rotational lift-off support, and the second changes only the gap.
- Final states match the reference: lift-off support released, gap closed. No diagnostics are raised.
- At the final iteration the out-of-balance force, moment and work at the free degrees of freedom are all exactly 0.0.
- The changes in displacement, rotation and reaction over the last iteration stay inside the recorded envelope for this group.
What it shows. Checks the supports’ final states, the iteration count and the balance of forces. Movements and reactions are not compared with a 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. The loop counts as converged only when no support changes state from one iteration to the next: the changed-support count must reach exactly 0, with no relative or absolute allowance, within at most 4 iterations. At the final iteration the out-of-balance force, moment and work at the free degrees of freedom must be 0.0, and the changes in displacement, rotation and reaction over the last iteration must stay inside a recorded envelope. Long values are shown here to seven significant figures; the tests compare the full values in the record.
One support’s change can alter the load path another support sees. Here the gap closes only after the rotation has been released, and the loop needs a third iteration to confirm that nothing else moves.
4.Run it yourself.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml multisupport_acceptance_inventory_uses_narrow_dec_046_policy
Hand calculation:
validation/hand_calcs/nonlinear/assembled_multi_support_cascade_gap_lift_off_acceptance.md.
Test record, with the recorded run of 2026-07-10:
nl-assembled-multi-dof-cascade-gap-lift-off-accepted-original.md.