# post_buckling

Family 9: a clamped-free column pushed past its Euler load, where it keeps carrying load while bending far sideways.

Exact anchor: the elastica of the buckled column (Timoshenko): the tip moves sideways delta/L = 0.22 at P/P_cr = 1.015,
0.59 at 1.15 and about 0.81 at 1.52. A straight column under exact load would stay straight in a solver, so the long
face also carries a small sideways load (IMPERFECTION of the axial load, spread along the length), which is the only
departure from the exact problem. Answers are read at P/P_cr = 1.06, 1.2 and 1.5 on one load curve.

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `t_over_L` | 0.01 - 0.03 |
| `w_over_t` | 1.2 - 4.0 |
| `nu` | 0.25 - 0.35 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `delta_106` | 0.04 % / 0.057 % / 0.057 % | max 1.4e-05 % | max - |
| `delta_120` | 0.015 % / 0.023 % / 0.023 % | max 3.5e-06 % | max - |
| `delta_150` | 0.0035 % / 0.0084 % / 0.0084 % | max 6.2e-07 % | max - |

## Checks

- points: 30 solved, 0 failed
- three-mesh studies: 6 (every 5th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0 %
- neighbour check: flagged 0, re-solved on a finer mesh 0, unresolved 0
- direction checks: 

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `delta_106_over_elastica` | 1.01 | 1.015 | 1.017 |
| `delta_120_over_elastica` | 1.002 | 1.004 | 1.004 |
| `delta_150_over_elastica` | 1 | 1.001 | 1.001 |

## Columns of points.csv

parameters, the answers, `<answer>_band` (relative), the hand-theory ratios, `mirror_err`, `equilibrium_err` (where a single reaction exists), `<answer>_loo_err` / `_neighbour_flag` (leave-one-out prediction from all other points), `<answer>_recheck_diff` / `_flag_resolved` (finer re-solve of a flagged point), `has_gci` / `has_similarity` / `has_calculix`, `nodes`, `solve_s`, `studio` (version).

Solved with NovaSolver Studio through the same commands an AI client uses over MCP; the first section says which solver and mesh. The claim is verification (the equations are solved within the band), not validation against tests.

## License

This data is licensed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Credit: NovaSolver, https://novasolver.jp/studio/verified/
Provided as is, without warranty. Design decisions remain the user's responsibility.