Part VI
Verification
B. Elements and loads · Inclined member transformation
A member runs from the origin to (1.0, 1.0, 0.0) m, at 45 degrees in the horizontal XY plane. Its stiffness is formed in local axes and then transformed to global axes. Does the solver find the correct member direction? Does the transformed stiffness matrix remain symmetric?
This page preserves a recorded benchmark and its expected values. The dated run below is not a new run of the current product.
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 |
|---|---|---|
| Start node | i | (0.0, 0.0, 0.0) m |
| End node | j | (1.0, 1.0, 0.0) m |
2.Method.
The local x axis is the vector from start node to end node, divided by its length. Its components are the direction cosines. A correct rotation of a symmetric stiffness matrix leaves it symmetric.
3.Results.
| Quantity | Expected |
|---|---|
| Component along global X | 0.7071068 |
| Component along global Y | 0.7071068 |
| Component along global Z | 0.0 |
| Global stiffness matrix | Symmetric |
The case record describes these checks:
- The solver’s local x axis has global X and Y components equal to the hand value.
- The transformed global stiffness matrix is symmetric.
- The two recorded components are equal to each other.
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. 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.Recorded command.
This command belongs to the linked case record and its recorded execution path. This website update did not rerun it. A historical command or result does not establish current product support.
cd projects/chirality-piping cargo test --manifest-path validation/benchmarks/mechanics/Cargo.toml inclined_member_transform_fixture_checks_direction_cosines_and_symmetry
Hand calculation:
validation/hand_calcs/mechanics/inclined_member_transform.md.
Test record, with the recorded run of 2026-07-10:
mech-inclined-member-transform.md.