Dynamic finite element analysis of bending-torsion coupled beams subjected to combined axial load and end moment
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Bibliographic record
Abstract
The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEMbased commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.001 | 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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