A High-Accuracy Empirical Formula for the Strain Concentration Factor in Countersunk Holes
Bibliographic record
Abstract
This paper presents a modified high-accuracy empirical formula for the strain concentration factor in a centrally-placed countersunk holes in isotropic plate under uniaxial tension. Finite Element Method (FEM) was used to investigate the effect of the problem geometric parameters including, plate width and thickness, as well as the hole radius, countersinking depth and angle on the strain concentration factor. The important influence of Poisson’s ratio was also thoroughly discussed. Based on the FEM-generated data and nonlinear regression, a general and high-precision equation for the strain concentration factor was developed. The formulation process was based on producing a general formula for computing the strain concentration factor with unknown coefficients. Such coefficients are determined by minimizing the relative error between the fitted equation and the FE data using nonlinear least squares method. The results of this newly-developed equation were validated with FEA. The comparison showed high accuracy of the present equation in evaluating strain concentration factor in countersunk holes with a relative approximate error of less than 7%. Besides, this equation was efficiently employed to test the various geometric and material parameters on the strain concentration value of countersunk holes. The results of the present equation were compared to the results of older equation available in literature. The comparison proved much higher accuracy of the present equation in evaluating strain concentration factor especially for deeper and larger countersunk holes than the previously published formula.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 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".