Simplified Stress Linearization Method, Maintaining Accuracy
Bibliographic record
Abstract
ASME PVP Code stress linearization is needed for assessment of primary and primary-plus-secondary stresses. The linearization process is not precisely defined by the Code; as a result, it may be interpreted differently by analysts. The most comprehensive research on stress linearization is documented in the work of Hechmer and Hollinger [1]. Recent non-mandatory recommendations on stress linearization are provided in Annex 5A of Section VIII, Division 2 of ASME PVP Code [2]. In the work of Kalnins [3] some linearization questions are discussed in two examples; the first is a plane-strain problem and the second is an axisymmetric analysis of primary plus secondary stress at a cylindrical-shell/flat-head juncture. Paper [3] concludes that for the second example the linearized stresses produced by Abaqus [5] diverge, therefore they should not be used for stress evaluation for this specific case. This paper revisits the axisymmetric analysis discussed in [3] and attempts to show that the linearization difficulties can be avoided. The paper explains in details the reason for the divergence; the Abaqus program does not linearize all stress components in axisymmetric elements; two stress components are calculated from assumed formulas and all others are linearized. It is shown that when the axisymmetric structure from [3] is modeled with 3D elements, the linearization results are convergent. Further, it is demonstrated that both axisymmetric and 3D modeling produce the same and correct stress Tresca stress, if the stress is evaluated from all stress components linearized, without any further modification. The stress evaluation of the axisymmetric model of [3] is the primary-plus-secondary-stresses evaluation for which the limit analysis described in [4] cannot be used. The paper shows how the original primary-plus-secondary-stresses problem can be converted into the equivalent primary-stress problem, that is for a problem for which limit analysis can be used; it is further shown how the limit analysis had been used for verification of the linearization results.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.009 |
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".