On Systematic Errors of Two-Dimensional Finite Element Modeling of Right Circular Planar Flexure Hinges
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Bibliographic record
Abstract
This paper discusses the finite element method (FEM) based modeling of the behavior of typical right circular flexure hinges used in planar compliant mechanisms. Such hinges have traditionally been approximated either by simple beams in the analytical approach or very often by two-dimensional (2D) plane stress elements when using the FEM. The three-dimensional (3D) analysis presented examines these approximations, focusing on systematic errors due to 2D modeling. It is shown that the 2D models provide only the lower (assuming the plane stress state) or the upper (assuming the plane strain state) limits of the hinge’s stiffness. The error of modeling a particular hinge by 2D elements (with either the plane stress or the plane strain assumptions) depends mainly on its depth-to-height ratio and may reach up to about 12%. However, this error becomes negligible for hinges with sufficiently high or sufficiently low depth-to-height ratios, in which either the plane strain or stress states dominate respectively. It is also shown that the computationally intensive 3D elements can be replaced, without sacrificing accuracy, by numerically efficient 2D elements if the material properties are appropriately manipulated.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it