The Wave Finite Element Method Applied to a One-Dimensional Linear Elastodynamic Problem With Unilateral Constraints
Bibliographic record
Abstract
The Wave Finite Element Method (WFEM) is implemented to accurately capture travelling waves propagating at a finite speed within a bouncing rod system and induced by unilateral contact collisions with a rigid foundation; friction is not accounted for. As opposed to the traditional Finite Element Method (FEM) within a time-stepping framework, potential discontinuous deformation, stress and velocity wave fronts are accurately described, which is critical for the problem of interest. A one-dimensional benchmark with an analytical solution is investigated. The WFEM is compared to two time-stepping solution methods formulated on a FEM semi-discretization in space: (1) an explicit technique involving Lagrange multipliers and (2) a non-smooth approach implemented in the Siconos package. Attention is paid to the Gibb’s phenomenon generated during and after contact occurrences together with the time evolution of the total energy of the system. It is numerically found that the WFEM outperforms the FEM and Siconos solution methods because it does not induce any spurious oscillations or dispersion and diffusion of the shock wave. Furthermore, energy is not dissipated over time. More importantly, the WFEM does not require any impact law to close the system of governing equations.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".