Axisymmetric indentation of an elastic thin plate by a rigid sphere revisited
Bibliographic record
Abstract
Abstract A simple analytical model based on a Kerr‐type differential relation is proposed to study the indentation problem of a circular elastic thin plate indented by a rigid sphere. Unlike some existing methods which matched two solutions inside and outside the contact zone, the present method is based on a simple differential relation between contact pressure and the normal deflection of the pressured surface of elastic plate, which holds both inside and outside the contact zone and makes it possible to analyze both zones by a single governing differential equation. Explicit relations between the contact‐zone radius, indentation displacement and indentation load are derived for different boundary conditions. The proposed model is validated by good agreement between the predicted results and some known data available in existing literature. In particular, the present model confirms that the indenter will lose contact with the plate around the center of the plate as the indentation load exceeds a certain critical value, and then the contact zone becomes to an annular zone. Detailed analytical and numerical results beyond existing literature are demonstrated for the annular contact zone regarding the critical contact‐zone radius, the width of annular contact zone and the associated contact pressure distribution.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".