Investigating Static Deflection of Axial Functionally Graded Non-Prismatic Beams Using the Rayleigh Method
Bibliographic record
Abstract
In this paper, Rayleigh method is utilized to compute the static deflection for simply supported, clamped-free, and free-clamped non-prismatic axial functionally graded (FG) beams under uniform distributed load.The non-prismatic beam was described assuming linear variation in width, height, or both, and the material distribution along the axial direction was defined using the power law model.A very excellent agreement was obtained when the Rayleigh method accuracy was compared with the results of the Finite Element Method (FEM) and the results of the previous literature.Results of the static deflection for axial functionally graded non-prismatic beams were displayed as a dimensionless form.The effects of material distribution, variation rate and supporting types were investigated.the results show that, generally, the maximum dimensionless static deflection is decreases at the same variation rate and any material distribution parameter.Also, when the material distribution parameter increases, the maximum dimensionless static deflection decreases at the same variation rate.The width variation has the maximum dimensionless static deflection comparing with the other variation cases.
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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 | 0.000 |
| 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 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".