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. A stop 0.01 mm beyond that end resists positive movement. The gap starts closed, with the end at the stop. A load of −2.0 N pulls the end away. The stop can push but cannot pull, so does the gap open, and where does the end settle?

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 and independent numerical comparison. 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.

2.Method.

With the gap closed, the first solve holds the end at the clearance, +0.01 mm. The reaction there is 100.0 × 0.01 − (−2.0) = +3.0 N. A stop that resists positive movement can bear only with a negative reaction. A positive reaction means the stop would have to pull the end onto itself, so the gap opens.

On the second iteration the end is free and moves −2.0 / 100.0 = −0.02 mm. That does not reach the +0.01 mm clearance, so the gap stays open, nothing changes state, and the loop has converged.

3.Results.

The case record describes these checks:

• The solve converges in exactly 2 iterations, ending with the gap open and a changed-support count of 0.
• On the first iteration the end is held at 0.01 mm and the reaction is 3.0 N, compared exactly.
• The final displacement is −0.02 mm and the final reaction is 0.0 N, compared exactly.
• 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.
• Any change in displacement or reaction over the last iteration stays inside the recorded envelope.

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. 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
cargo test --manifest-path validation/benchmarks/nonlinear/Cargo.toml dec_067_transition_fixtures_witness_state_switched_and_bounded_outcomes

Hand calculation: validation/hand_calcs/nonlinear/assembled_gap_lift_off.md. Test record, with the recorded run of 2026-07-10: nl-assembled-gap-lift-off-original.md.