Lower Bound Limit Load Determination: The mβ-Multiplier Method
Bibliographic record
Abstract
The existing lower bound limit load determination methods, that are based on linear elastic analysis such as the classical and mα-multiplier methods, have a dependence on the maximum equivalent stress. These methods are therefore sensitive to localized plastic action, which occurs in components with thin or slender construction, or those containing notches and cracks. Sensitivity manifests itself as relatively poor lower bounds during the initial elastic iterations of the elastic modulus adjustment procedures, or oscillatory behavior of the multiplier during successive elastic iterations leading to limited accuracy. The mβ-multiplier method proposed in this paper starts out with Mura’s inequality that relates the upper bound to the exact multiplier by making use of the “integral mean of yield.” The formulation relies on a “reference parameter” that is obtained from considering a distribution of stress rather than a single maximum equivalent stress. As a result, good limit load estimates have been obtained for several pressure component configurations.
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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 | 0.004 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".