A Size-Dependent Continuum Model for Nanoscale Circular Plates
Bibliographic record
Abstract
Nanoscale circular plates are encountered in several nanotechnology-based devices such as nanoelectromechanical systems. Structures are size dependent at nanoscale due to surface energy effects. It is possible to capture such size dependence through special continuum models. In this paper, the Gurtin-Murdoch continuum theory is applied to develop a new continuum mechanics model for static deformation of thin and thick circular nanoplates. The relevant governing equations are established from basic principles. It is shown that the governing equations possess a closed-form analytical solution that makes the current approach suitable for device analysis and design. A series of closed-form analytical solutions is presented for static bending of thin and thick plates under common static loading (uniformly distributed and center point) and boundary conditions (simply supported and clamped edges). The analytical solution for a thin plate supported by a linear elastic substrate is also presented. Deflection profiles of selected silicon and aluminum plates are presented and compared with the classical plate theory results to examine the salient features of mechanical response and influence of surface elastic moduli, surface residual stress, and boundary conditions.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".