Numerical investigations into static and quasistatic problems of two-dimensional dry elastic frictional contact
Bibliographic record
Abstract
A numerical-modelling method is developed to investigate the stress of the static-equilibrium state of the two-dimensional frictional contact problem achieved through a quasistatic process of increasing loading. The problem of relative tangential displacement between particles on the two contact surfaces is addressed. This scheme relies on solving each of the two contact solids in turn and iterating back and forth. The solutions for the two elastic bodies are connected through the surface traction and surface deformation. The contact surface is approximated by a cubic spline, and friction is modelled using the classical Coulomb friction law. Variational inequalities and finite-element methods are used to implement this scheme and are solved by an optimization method. In addition, the distinction between Cauchy stress and PiolaKirchoff stress is taken into account and discussed. A numerical investigation is conducted into the stress dependence on the loading conditions and geometries of the solids. The results from the numerical examples deviate from Hertz theory and previous reports. Stress is shown to be sensitive to the loading distribution and geometry of contact solids. Therefore, it suggests that an accurate analysis of the dry frictional contact problem requires a refined knowledge of the loading conditions and the total geometry of both solids. PACS Nos.: 03.40D, 46.30P, 62.20P
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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) | 0.000 | 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 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".