Friction and a gap at one tip — SWBPIPE verification

Part VI · VerificationVI–E12

Part VI

Verification

E. Algorithm and software checks · Friction and a gap at one tip

A frame member is fixed at its root. Tip forces are 10.0 N along x and 1.0 N along y. In x, friction has μ = 0.30 and given normal reaction 20.0 N. In y, a gap has clearance 0.0002 mm. Friction starts sticking, and the gap starts open. Where do the supports 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 check. The recorded test exercises nonlinear support state or assembled-loop behavior in its benchmark crate. It does not exercise desktop authoring.

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Friction here acts along one axis, with its normal force given or taken from another support. In a real line, friction belongs to the rest itself. It acts against the resultant sliding in the support plane (Part II H, Status).

Fig. VI–E12.—Friction and a gap at one tip

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
Friction support	—	U_x
Gap support	—	U_y
Friction coefficient	μ	0.30
Normal reaction (given)	N	20.0 N
Friction limit	μN	6.0 N
Gap clearance	c	0.0002 mm
Initial friction state	—	sticking
Initial gap state	—	inactive (open)

2.Method.

The friction limit is 0.30 × 20.0 = 6.0 N. The 10.0 N axial force is more than that, so the support slides. The gap closes. Both supports change on the first iteration, and neither changes on the second.

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.

μN = 0.30 × 20.0 = 6.0 N(1)

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 friction state	sliding
Final gap state	active (closed)
Converged	true
Diagnostic	none

The case record describes these checks:

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: friction sliding, gap 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. 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, rotation 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 multisupport_acceptance_inventory_uses_narrow_dec_046_policy

Hand calculation: validation/hand_calcs/nonlinear/assembled_multi_support_friction_gap_acceptance.md. Test record, with the recorded run of 2026-07-10: nl-assembled-multi-dof-friction-gap-accepted-original.md.