A semianalytical solution for the bending of clamped laminated doubly curved or spherical panels
Bibliographic record
Abstract
A semianalytical solution is presented for bending of moderately thick fully clamped laminated doubly curved panels using the extended Kantorovich method (EKM).The panel is subjected to uniform and nonuniform distributed loading and cut from a rectangular platform.Based on the first-order shear deformation theory, five highly coupled second-order partial differential equations in terms of displacement components are derived.Assuming separable functions for panel displacements together with the EKM converts the governing equations into double sets of ordinary differential equations with constant coefficients in terms of x and y.The resulting ODE systems are then solved iteratively until a level of prescribed convergence is achieved.Closed-form solutions can be presented for ODE systems in each iteration.Efficiency and rapid convergence of the solution technique are examined using several examples.Predictions of both deflection and stress resultants show very good agreement with other available results in the literature.It is also shown that the same formulation and solution method can be used to obtain results for spherical and cylindrical panels and rectangular plates.
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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 | 0.001 |
| 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 | 0.000 | 0.000 |
| 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".