IMPLEMENTATION OF CONSISTENT UPDATED LAGRANGIAN FORMULATION FOR STATIC ANALYSIS OF GEOMETRICALLY NONLINEAR BEAM
Bibliographic record
Abstract
In this paper, the consistent updated Lagrangian (CUL) formulation used for solving large-displacement non-linear problems is compared with the total Lagrangian (TL) and the updated Lagrangian (UL) formulations. This comparison indicates that these formulations use different reference configurations for developing stiffness and internal load vectors but yield identical terms. The equivalence of the three Lagrangian formulations was confirmed by developing the governing equilibrium equations for the CUL formulation using the continuum mechanics approach. For a two-noded, two-dimensional, large displacement-small strain Euler-Bemoulli beam element, the CUL finite element formulation of the equilibrium equations was developed to illustrate the procedure used to obtain the stiffness matrix and internal load vectors. All three finite element Lagrangian formulations were implemented and tested for static analysis of two-dimensional, Euler-Bemoulli straight cantilever beam subjected to a transverse tip load at the free end. They all gave identical results, which were comparable to those obtained using a co-rotational formulation.
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 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 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| 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".