Two gaps closing in opposite senses

Part VI · VerificationVI–E17

Part VI

Verification

E. Algorithm and software checks · Two gaps closing in opposite senses

A single frame member is fixed at its root. Its tip is pushed by 10.0 N along x and by −1.0 N along y. There are no other nonlinear supports, only two gaps of 0.0002 mm each. The gap in x closes on positive movement; the gap in y closes on negative movement. Both start open. Does the solver close both, each in its own sense?

Fig. VI–E17.—Two gaps closing in opposite senses

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 axial force	F_x	10.0 N
Tip transverse force	F_y	−1.0 N
Positive-side gap	—	U_x, closes on positive displacement
Negative-side gap	—	U_y, closes on negative displacement
Positive gap clearance	c_x	0.0002 mm
Negative gap clearance	c_y	0.0002 mm
Initial states	—	both inactive (open)

2.Method.

On the first iteration both gaps close. On the second iteration neither changes, so the loop has converged.

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.

Expected outcome (the reference gives states, counts and residuals, not displacements or reactions)
Quantity	Expected
Changed supports, iteration 1	2
Final changed-support count	0
Iteration count	2
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 positive-side gap state	active (closed)
Final negative-side gap state	active (closed)
Converged	true
Diagnostic	none

The tests check that:

The solve converges in exactly 2 iterations: 2 supports change state on the first iteration and none on the last.
Final states match the reference: both gaps 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.

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_opposing_gaps_acceptance.md. Test record, with the recorded run of 2026-07-10: nl-assembled-multi-dof-opposing-gaps-accepted-original.md.