Structural Optimization Under Variable Loading Conditions
Bibliographic record
Abstract
Abstract The problem of structural optimization under variable loading conditions is discussed here. We assume a linearly-elastic structure subject to one single load of constant magnitude but of arbitrary orientation. Moreover, we assume that the structure is discretized by finite elements. The result of this study is an optimality criterion: the eigenvalues of the stiffness matrix of the optimum structure observe a minimum variance. In other words, the optimum structure under variable load must have a stiffness matrix that is as close as possible to isotropy. Furthermore, in order to implement the foregoing criterion, we introduce a novel method of automatic mesh generation, that is based on the concept of penalty functions of nonlinear programming. Finally, we illustrate these concepts by means of the optimization of a triangular lamina of given side lengths, with an elliptical hole centered at its centroid, of a prescribed area, the design parameters being the semiaxes of the ellipse and the orientation of these axes with respect to the edges of the lamina.
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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) | 0.029 | 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".