Inelastic Stress Analysis of Curved Beams with Bending and Shear Coupling
Bibliographic record
Abstract
The inelastic stress analysis of curved beams under pure bending has been extensively studied in the past few years. Nevertheless, the analysis for those under end shear, or mo ment and shear coupling, are not yet available. In this paper, the analytical model for inelastic stress analysis of symmetrical curved beams with bending and shear coupling is derived. This problem arises from the investigation of the inelastic behaviour of an in-p lane flexu ral damper consisting of a circular arch with two straight arms. In -plane lateral forces applying to the end of the arm makes the arch a circular cantilever subjected to mo ment and shear simultaneously. Extended fro m the classical theory of elasticity, the proposed computational model adopts the generalized Hook's law in plane stress with consideration of the plastic strains defined by the total deformation theory. The swift -type nonlinear hardening law is considered for the inelastic constitutive relations of the material with its behaviour governed by von Mises' yield criterion. With the introduction of a certain form of Airy stress function that satisfies the compatibility equation in polar coordinates, the strain -compatib ility equation with the corresponding boundary conditions can be simplified as a second -order ordinary differential equation of a properly defined generalized stress function dependent on radius of the wide curved beam. Solution of this ODE equation becomes a boundary -valued problem that can be solved numerically in both elastic and inelastic stages. To validate the proposed mode l, a p reliminary n umerical study of the stress analysis in the elastic stage has been conducted. Encouragingly, the numerical solution agrees perfectly with its analytical counterpart given by classical theory of elasticity.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".