Part VI
Verification
E. Algorithm and software checks · Axial gap closes
A straight member 1.0 mm long has axial stiffness 100.0 N/mm and one fixed end. Its other end can move only axially and carries a 10.0 N push. A stop stands 0.05 mm beyond that end. The end can move through this clearance without contact resistance. The gap starts open. Does the end reach the stop and settle with the gap closed?
This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.
These recorded transitions and free-degree residuals do not establish general equilibrium or convergence for other models.
Support state check. The recorded test exercises nonlinear support state or assembled-loop behavior in its benchmark crate. It does not exercise desktop authoring.
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 case record describes these checks:
- 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. Compares final support states, the iteration count, and force balance. It does not compare movements or reactions 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 between iterations. The changed-support count must reach exactly 0 within at most 4 iterations, with no relative or absolute allowance. At the final iteration, out-of-balance force, moment and work at free degrees of freedom must be 0.0. Changes in displacement and reaction over the last iteration must stay inside the recorded envelope. 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 archived source at 462f66975d36cd10d5b8455193ada9517d28d353. Use a checkout of that exact revision. This edition did not run the command. The recorded result does not establish current product support.
git checkout --detach 462f66975d36cd10d5b8455193ada9517d28d353 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.