A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems
Bibliographic record
Abstract
Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq–Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor (ψ), which accounts for the normal load. The expression ψ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was −21.90% for a shear load correction (Poisson coefficient ν=0.3), and introducing the ψ factor reduced the deviation to −9.55%, while for ν of 0.15, the maximum error was −11.30%, which was reduced to +0.60% with the ψ factor. This study introduces the factor ψ in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".