On a consistent dynamic finite-strain shell theory and its linearization
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Bibliographic record
Abstract
In this paper, a dynamic finite-strain shell theory is derived, which is consistent with the three-dimensional (3-D) Hamilton’s principle with a fourth-order error under general loadings. A series expansion of the position vector about the bottom surface is adopted. By using the bottom traction condition and the 3-D field equations, the recursive relations for the expansion coefficients are successfully obtained. As a result, the top traction condition leads to a vector shell equation for the first coefficient vector, which represents the local momentum-balance of a shell element. Associated weak formulations, in connection with various boundary conditions, are also established. Furthermore, the derived equations are linearized to obtain a novel shell theory for orthotropic materials. The special case of isotropic materials is considered and comparison with the Donnell–Mushtari (D-M) shell theory is made. It can be shown that, to the leading order, the present shell theory agrees with the D-M theory for statics. Thus, the present shell theory actually provides a consistent derivation for the former one without any ad hoc assumptions. To test the validity of the present dynamic shell theory, the free vibration of a circular cylindrical shell is studied. The results for frequencies are compared with those of the 3-D theory and excellent agreements are found. In addition, it turns out that the present shell theory gives better results than the Flügge shell theory (which is known to provide the best frequency results among the first-approximation shell theories).
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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 | 0.000 | 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 | 0.000 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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