On the static analysis of constrained structural systems
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Bibliographic record
Abstract
Complete structures might contain so many degrees of freedom that it would be infeasible to perform a structural analysis. The derivation of the equilibrium equations of an entire structure to utilize kinematical compatibility conditions at the interfaces of the substructures requires complicated intermediate processes or numerical schemes for determining multipliers. This study derives an explicit matrix form of the equilibrium equations of structural systems subjected to constraints like compatibility conditions or linear displacement relations. The equation is obtained by minimizing a quadratic form of the variation in unconstrained and constrained displacements with respect to all constrained displacements that satisfy the constraints. And the physical meaning of the constraint forces required to satisfy the constraints is investigated. The validity of the proposed method is illustrated by several applications.Key words: constraints, compatibility, equilibrium equation, generalized inverse.
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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 | 0.001 | 0.001 |
| 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) | 0.000 | 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 it