Part VI
Verification
E. Algorithm and software checks · Axial gap closes
A straight member 1.0 mm long, with an axial stiffness of 100.0 N/mm, is fixed at one end. The other end can move only along the member’s axis. It is pushed along the axis by 10.0 N. A stop stands 0.05 mm beyond the free end, so the end can move that far before it meets any resistance. The gap starts open. Does the end reach the stop, and does the solver settle with the gap closed?
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 |
|---|---|---|
| Node count | — | 2 |
| Member length | L | 1.0 mm |
| Axial stiffness | k | 100.0 N/mm |
| Applied axial force | F | 10.0 N |
| Gap clearance | c | 0.05 mm |
| Maximum iterations | — | 4 |
| Active-set residual tolerance | — | 0.0 (count) |
| Initial state | — | inactive (gap open) |
2.Method.
With the gap open, the first solve is free, and the end moves further than the 0.05 mm clearance. The gap therefore closes. The second solve holds the end at the clearance. The gap stays closed, nothing changes state, and the loop has converged after two iterations.
3.Results.
| Quantity | Expected |
|---|---|
| Iteration count | 2 |
| Final changed-support count | 0.0 |
| Final state | active (gap closed) |
| Converged | true |
The tests check that:
- The solve converges in exactly 2 iterations, ending with the gap closed and a changed-support count of 0.
- At the final iteration the out-of-balance force, moment and work at the free degrees of freedom are all exactly 0.0.
- The solve carries no notice that its tolerance is unset.
- The displacement changes over the last iteration, and that change stays inside the recorded envelope.
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 change in displacement 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.
4.Run it yourself.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml assembled_global_loop_seed_cases_converge_under_governed_policy cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml assembled_convergence_observations_record_measured_fixture_values_only cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml assembled_force_displacement_residual_observations_use_free_dof_force_moment_thresholds
Hand calculation:
validation/hand_calcs/nonlinear/assembled_gap_closure.md.
Test record, with the recorded run of 2026-07-10:
nl-assembled-gap-closure-original.md.