Uniqueness of solutions in the boundary value problems of bending of thin micropolar plates with surface effects
Bibliographic record
Abstract
We propose a micropolar thin plate theory that incorporates surface elasticity effects to take into account simultaneously the contribution of high surface-to-volume ratios and the influence of microstructural mechanics at micro/nano scales. Using a direct averaging approach across the plate’s thickness, we derive governing equations that consider the elastic properties of the upper and lower surfaces, treated as two-dimensional micropolar bodies. The boundary value problems are analyzed, with particular attention to solution uniqueness, as a first step toward establishing the well-posedness of the model. A simplified example demonstrates the mathematical formulation and compares the results with classical plate theory. A numerical example highlights the combined effects of surface elasticity and micropolar characteristics as the plate thickness varies, illustrating the influence of these factors on effective bending stiffness. The results reveal that surface and micropolar effects contribute to deformations by varying magnitudes, depending on material properties and plate size.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| 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) | 0.000 | 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 teacher head, 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".