Free vibration analyses of functionally graded plates based on improved refined shear and normal deformation theory considering thickness stretching effect using Airy stress function
Bibliographic record
Abstract
In this paper, an improved refined shear and normal deformation theory is used in order to investigate the vibration behavior of functionally graded rectangular plates. In this theory, displacements of various points of plate are assumed to be due to in-plane displacements of the middle plane and transverse displacement. Transverse displacement is divided into three parts: bending, shear, and thickness stretching. Using the Airy stress function, corresponding to the compatibility equation, and employing the extended Hamilton’s principle, in-plane displacements are omitted from the equations of motions. Thus, the proposed approach uses only three-unknowns in the displacement field. The results of vibration analysis using the proposed approach are in excellent agreement with three-dimensional and quasi-three-dimensional solutions containing a greater number of unknowns to consider the thickness stretching effect. Static and dynamic behavior of wide variety of thin and thick functionally graded plates can be studied using the proposed approach in which not only the number of variables is reduced, but also the contribution of bending, shear, and thickness stretching are completely clarified.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 | 0.001 |
| 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".