An Elastic Wedge Under Moment Loading: The Carothers Paradox Revisited
Bibliographic record
Abstract
Abstract In this paper, a semi-infinite wedge of arbitrary angle under moment loading is studied. The moment may be located at any position within the wedge. First, to treat this issue in a general sense, the fundamental solution for a pointwise moment is derived by virtue of an assembly of deliberately distributed four concentrated forces. Then, using conformal mapping technique, the analytical solution for the semi-infinite wedge interacting with the pointwise moment is derived. Based on this solution, the wedge subjected to any moment loading is formulated. As an application, the Carothers problem, namely, the wedge vertex subjected a concentrated moment is analyzed. To resolve the so-called the Carothers paradox, a modified and practical model is proposed. The solutions developed in this study provide a basic block to study the problems of a wedge under complex moment loading conditions. Our results show that the stress distribution behavior distanced from the wedge vertex is categorically determined by its open angle.
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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 | 0.001 | 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 | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".