Refined three-variable theory for the bending response of multidirectional functionally graded nanobeams
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Bibliographic record
Abstract
A new and improved shear deformation theory, featuring three variables and a built-in correction factor, is introduced to study the bending behavior of two-directional functionally graded (FG) beams. The displacement field is developed using the foundational ideas of Euler–Bernoulli beam theory (EBT). This work explores two types of coated FG nanobeams: hardcore (HC) and softcore (SC). Three patterns of material distribution are analyzed: a bidirectional setup, a unidirectional transverse layout, and a unidirectional axial design. To capture small-scale effects, the strain gradient nonlocal elasticity theory is applied. The governing equilibrium equations for the nanobeams are established through the principle of total potential energy. A sophisticated solution method, utilizing Galerkin’s approach, is used to effectively handle different boundary conditions. The FG beam is represented as resting on an elastic foundation, characterized by the Winkler, Pasternak, and Kerr models. This study offers a thorough assessment of how these elements together affect the critical buckling loads of nanobeams.
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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 | 0.001 | 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 it