A geometrically nonlinear Euler–Bernoulli beammodel within strain gradient elasticity with isogeometric analysis and latticestructure applications
Bibliographic record
Abstract
The nonlinear governing differential equation and variational formulation of the Euler-Bernoulli beam model are formulated within Mindlin's strain gradient elasticity theory of form II by adopting the von Kármán strain assumption.The formulation can retrieve some simplified beam models of generalized elasticity such as the models of simplified strain gradient theory (SSGT), modified strain gradient theory (MSGT), and modified couple stress theory (MCST).Without the presence of nonlinear terms, the resulting linear differential equation is solvable by analytical means, whereas the mathematical complexity of the nonlinear problem is treated with the Newton-Raphson iteration and a conforming isogeometric Galerkin method with C p-1 -continuous B-spline basis functions of order p ≥ 3. Through a set of numerical examples, the accuracy and validity of the present theoretical formulation at linear and nonlinear regimes are confirmed.Finally, an application to lattice frame structures illustrates the benefits of the present beam model in saving computational costs, while maintaining high accuracy as compared to standard 2D finite element simulations.
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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) | 0.001 | 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 | 0.001 |
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".