To Clarify Decision on Action of Concentrated Force to Elastic Quarter-Space for Arbitrary Poisson’s Ratio
Bibliographic record
Abstract
Previously, the author obtained an analytical solution for determining the vertical displacements of the homogeneous isotropic quarter-space face, which is affected by a vertical concentrated force. This expression gave an exact solution for determining the vertical displacements of a quarter-space face made of incompressible material and an approximate solution for a Poisson ratio different from 0.5. Later, in the published paper by S. V. Bosakov and P. D. Skachek “Action of Concentrated Force on 1/8 of Homogeneous Isotropic Space”, it was shown that by combining solutions for determining the vertical displacements of a quarter-space and a half-space from the action of concentrated forces, one can find vertical displacements for one-eighth face of a homogeneous isotropic space. The resulting expressions allow solving contact problems for non-classical domains in the form of a quarter of a space and one eighth of a space. Below, the author obtains the first approximation for displacements of a quarter-space face from the action of a vertical concentrated force. In this paper, the author gives the first approximation for determining the vertical displacements of a quarter-space face from the action of a vertical concentrated force, widely using the special approximation method developed in the works of V. M. Alexandrov and allowing to calculate successfully improper integrals. The constructed graphs show good results when determining displacements with a Poisson’s ratio different from 0.5 and equal to 0.5. It should be noted that the approach indicated in the paper by S. V. Bosakov and P. D. Skachek can be successfully used in determining all displacements of the faces of one-eighth face of a homogeneous isotropic sharpened forces tangent to the edge of a quarter-space and this will allow to solve contact problems taking into account friction forces in the contact zone of the beam or plate.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".