Numerical Investigation of the Flutter of a Spherical Shell
Bibliographic record
Abstract
In this study, aeroelastic analysis of a spherical shell subjected to external supersonic airflow is carried out. The structural model is based on a combination of the linear spherical shell theory and the classic finite element method (FEM). In this hybrid method, the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Therefore, the number of elements chosen is a function of the complexity of the structure. Convergence is rapid. It is not necessary to choose a large number of elements to obtain good results. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The linear mass, stiffness, and damping matrices are found using the hybrid finite element formulation. Aeroelastic equations are numerically derived and solved. The results are validated using the numerical and theoretical data available in literature. The analysis is accomplished for spherical shells with different boundary conditions, geometries, flow parameters, and radius to thickness ratios. the results show that the spherical shell loses its stability through coupled-mode flutter. This proposed hybrid FEM can be used efficiently for the design and analysis of spherical shells employed in high speed aircraft structures.
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How this classification was reachedexpand
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)
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 teacher head, 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".