Using Bézier curves to model gradual stiffness transitions in nonlinear elements: Application to self‐centering systems
Bibliographic record
Abstract
Abstract A number of techniques are available for modelling nonlinear elements, but most available hysteretic rules do not capture the gradual stiffness changes that are typical of physical systems. In particular, there has not previously been a hysteretic rule with rounded hysteretic corners that could be used to model self‐centering elements, where multiple stiffness changes occur within one loading cycle. This paper presents a new hysteretic rule that allows the gradual stiffness transitions that occur in real systems to be modelled. In this paper, the rule is formulated for flag‐shaped hystereses, but it is shown that the same model also produces hystereses that can be used to model systems that are not self‐centering. The same technique could also be applied to round the corners of different backbone hystereses. A previous study has shown how abrupt stiffness changes can cause very large acceleration spikes, particularly in self‐centering systems. This paper shows that acceleration spikes due to stiffness changes may be reduced by designing systems to change stiffness more gradually, and that this typically has little effect on other aspects of the seismic response. When modelling structural systems, especially if they are self‐centering, sharp‐cornered hysteretic models may be used for initial analysis, but round‐cornered hysteretic models should be considered when using nonlinear rotational springs or when accelerations are of particular importance. Copyright © 2011 John Wiley & Sons, Ltd.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".