Evaluation of fracture parameters for crack problems in fgm by a meshless method
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Bibliographic record
Abstract
A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2D), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static thermal and transient elastodynamic problems are considered. For time-dependent problems, the Laplace transform technique is utilized. The analyzed domain is divided into small subdomains of circular shapes. A unit step function is used as the test function in the local weak form. It leads to Local Integral Equations (LIE) involving a domain-integral only in the case of transient dynamic problems. The Moving Least Squares (MLS) method is adopted for approximating the physical quantities in the LIE. Efficient numerical methods are presented to compute the fracture parameters, namely, the stress intensity factors and the $ T$-stress, for a crack in Functionally Graded Materials (FGM). The path-independent integral representations for stress intensity f actors and $ T$-stresses in continuously non-homogeneous FGM are presented.
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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 | 0.005 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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