The M-Beta Multiplier Method for Limit Load Determination of Components With Local Plastic Collapse
Bibliographic record
Abstract
The mβ-multiplier method based on Mura’s extended variational principles in plasticity relies on a reference stress that is obtained from an entire stress distribution in a structure. The method is relatively insensitive to components that undergo localized plastic action and generates limit load bounds that are better than the classical and mα-multiplier methods. The multiplier mβ is determined by evaluating a reference parameter βR, which may be difficult to determine if the stress distribution obtained using elastic modulus adjustment procedures does not converge to a limit type of distribution. In this paper, physical insights relating to the reference parameter βR are provided by linking the concept of reference volume to the local collapse of the structure. As well, a systematic procedure to identify the converged limit state is presented. The mβ-multiplier method, developed in conjunction with the reference volume concept, is applied to a number of cracked component configurations. The results are compared with the corresponding inelastic finite element analysis.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".