Comprehensive Stiffness of Prestressed Lattice Materials
Bibliographic record
Abstract
Several approaches to obtain the comprehensive stiffness of finite frameworks are present in literature; yet, the formulation has not been addressed for lattice materials and infinitely periodic structures. The objective of this paper is to introduce a systematic method to calculate the comprehensive stiffness of prestressed, infinitely periodic, structures and lattice materials with pin- and rigid-jointed connectivity. We first derive the comprehensive stiffness of a finite framework through the superposition of its material and nonlinear geometrical stiffness. By using the Bloch's theorem, we derive the irreducible form of the stiffness system of the finite framework, which represents the stiffness behaviour of the corresponding infinite, periodic assembly. Finally, the comprehensive stiffness of the infinite lattice is homogenized to generate the stiffness characteristics of the lattice material. A detailed example is provided to show the application of the methodology. Closed-form expressions of the elastic properties are presented for 12 planar lattices.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".