Limit Analysis for Anisotropic Solids Using Variational Principle and Repeated Elastic Finite Element Analyses
Bibliographic record
Abstract
Many structural components, such as rolled sheets, directionally solidified superalloys and composites, are made of anisotropic materials. The knowledge of limit load is useful in the design and the sizing of these components and structures. This paper presents the extension of the modified mα-method to anisotropic materials. Mura’s variational principle is employed in conjunction with repeated elastic finite element analyses (FEA). The secant modulus of the discretized finite elements in the reference direction in successive elastic iterations is used to estimate the plastic flow parameter for the anisotropic components. The modified initial elastic properties are adopted to ensure the “elastic” stress fields satisfy the anisotropic yield surface. Using the notion of “leap-frogging” to limit state, improved lower-bound limit loads can be obtained. The formulation is applied to two anisotropic components, and the limit load estimates are compared with those using elastic compensation method and inelastic FEA.
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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 | 0.000 | 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) | 0.001 | 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 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".