Two spans with opposing gaps — SWBPIPE verification

Part VI · VerificationVI–E21

Part VI

Verification

E. Algorithm and software checks · Two spans with opposing gaps

Two frame members in a line make a two-span chain of three nodes, fixed at the first. The tip is pushed by 10.0 N along x and −1.0 N along y. The middle node faces a 0.0002 mm gap in x that closes on positive movement. The tip faces a 0.0002 mm gap in y that closes on negative movement. Both start open. Does each close, on its own node and in its own sense?

Fig. VI–E21.—Two spans with opposing gaps

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	—	3
Span (element) count	—	2
Tip axial force	F_x	10.0 N
Tip transverse force	F_y	−1.0 N
Middle-node gap	—	node 1, U_x, closes on positive displacement
Tip gap	—	node 2, U_y, closes on negative displacement
Middle-node gap clearance	c₁	0.0002 mm
Tip gap clearance	c₂	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 middle-node gap state	active (closed)
Final tip 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_two_span_opposing_gaps_acceptance.md. Test record, with the recorded run of 2026-07-10: nl-assembled-multi-dof-two-span-opposing-gaps-accepted-original.md.