Exact Finite Element for Nonuniform Torsion of Open Sections
Bibliographic record
Abstract
A finite-element formulation that captures both the St. Venant and warping torsional effects of open sections is developed. The formulation is applicable to prismatic thin-walled open sections commonly used in steel construction and is able to represent general torsional and warping end restraints. The element has two end nodes, each having two degrees of freedoms, and featuring continuity of the first derivative of the angle of twist (C1 continuity). A family of hyperbolic interpolation functions is adopted in the derivation in lieu of conventional polynomial displacement interpolation schemes. The stiffness matrix and the associated energy equivalent load vector are demonstrated to yield nodal generalized displacements and forces in exact agreement with classical solutions for any externally applied twisting moment distribution. Consequently, the formulation allows the adoption of coarser subdivisions than those needed in other finite-element formulations while preserving the exactness of the results. The formulation is simple and provides a basis to assess the quality of results of other approximate finite-element solutions. The implications of the exactness of the formulation are discussed and illustrated through examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".