Refined three-variable theory for the bending response of multidirectional functionally graded nanobeams
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.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 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".