POLYNOMIAL SHAPE FUNCTIONS AND NUMERICAL METHODS FOR FLEXIBLE MULTIBODY DYNAMICS*
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Bibliographic record
Abstract
The use of Taylor polynomials as shape functions in a Rayleigh–Ritz discretization of flexible beams in dynamic multibody systems has been previously investigated [[1] Valembois, R. E., Fisette, P. and Samin, J. C. 1997. Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics. Nonlinear Dynam., 12: 367–397. [Crossref], [Web of Science ®] , [Google Scholar] [2] Saad, M., Piedboeuf, J.-C. and Akhrif, O. in press. Comparison of Different Shape Functions in Assumed-Mode Models of a Flexible Slewing Beam. Mechanism Mach. Theory, [Google Scholar]]. This approach is relatively simple, but it was found to cause some ill-conditioning problems in the numerical solution of the system equations. In this paper, two solutions to these problems are presented. First, better-behaved system equations can be obtained by using orthogonal Chebyshev or Legendre polynomials in place of Taylor polynomials. Secondly, a judicious choice of numerical solver can reduce or eliminate the ill-conditioning problems. Two examples are used to demonstrate these findings.
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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 |
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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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