Analytical and Finite Element Multi-Shell Modelling of an Intervertebral Disc
Bibliographic record
Abstract
The objective of this study is to develop an analytical model of an intervertebral disc capable of predicting stresses and deformations in the anulus fibrosus. The anulus fibrosus is treated as a multi-shell structure for which membrane theory applies and the junction with the end plates assumed rigid is treated with beam on elastic foundation theory. The displacements and stresses of the anulus fibrosus, when the disc is subjected to a compressive force are investigated. The discontinuity stresses are superimposed to those of the membrane stresses to estimate the stress state of the anulus fibrosus. The analytical results are compared to those of a finite element model for validation. The analytical and the finite element models show the same general trend, but their relative difference in estimating the stresses is rather high. However, both models show that the highest circumferential stress is located on the innermost lamella at the transverse plane. Furthermore, the stresses decrease through the disc thickness and at the vicinity of the endplates. These results allow to indicate, analytically, the location for maximal principal stresses in the anulus fibrosus.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".