Imposed displacement on a spring — SWBPIPE verification

Part VI · VerificationVI–B4

Part VI

Verification

B. Elements and loads · Imposed displacement on a spring

A single linear spring of stiffness 150.0 N/m is pushed through a prescribed displacement of 0.04 m. What reaction does it develop?

The case also checks the solver’s boundary preparation. The spring and the imposed displacement must be kept as two separate entries, each of the right kind. No frame system is solved.

Read with

The case checks the spring boundary prepared for the solver. The program’s own solve path does not yet accept imposed movements (Status).

Fig. VI–B4.—Imposed displacement on a spring

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
Spring stiffness	k	150.0 N/m
Imposed displacement	u	0.04 m

2.Method.

For a linear spring the reaction is stiffness times displacement.

R = ku = 150.0 × 0.04 = 6.0 N(1)

3.Results.

Spring reaction
Quantity	Expected
Spring reaction magnitude	6.0 N

The tests check that:

Boundary preparation accepts the spring and the imposed displacement without blocking.
Exactly one spring and one imposed displacement are recorded.
The prepared stiffness times the prepared displacement matches the reference reaction.

What it shows. Checks the loads or boundary conditions prepared for the solver against a hand calculation. No system is solved.

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. Each computed value must match the reference within an absolute difference of 1.0 × 10⁻⁹ in the case’s own units; counts and structural outcomes must match exactly. 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/mechanics/Cargo.toml imposed_displacement_fixture_prepares_support_boundary

Hand calculation: validation/hand_calcs/mechanics/imposed_displacement_spring.md. Test record, with the recorded run of 2026-07-10: mech-imposed-displacement-spring.md.