ELASTIC FLEXURAL-TORSIONAL BUCKLING ANALYSIS USING FINITE ELEMENT METHOD AND OBJECT-ORIENTED TECHNOLOGY WITH C/C++
Bibliographic record
Abstract
Flexural-torsional buckling is an important limit state that must be considered in structural steel design. Flexural-torsional buckling occurs when a structural member experiences significant out-of-plane bending and twisting. This type of failure occurs suddenly in members with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. Flexural-torsional buckling loads may be predicted using energy methods. This thesis considers the total potential energy equation for the flexural-torsional buckling of a beam-column element. The energy equation is formulated by summing the strain energy and the potential energy of the external loads. Setting the second variation of the total potential energy equation equal to zero provides the equilibrium position where the member transitions from a stable state to an unstable state. The finite element method is applied in conjunction with the energy method to analyze the flexural-torsional buckling problem. To apply the finite element method, the displacement functions are assumed to be cubic polynomials, and the shape functions are used to derive the element stiffness and element geometric stiffness matrices. The element stiffness and geometric stiffness matrices are assembled to obtain the global stiffness matrices of the structure. The final finite element equation obtained is in the form of an eigenvalue problem. The flexural-torsional buckling loads of the structure are determined by solving for the eigenvalue of the equation. The finite element method is compatible with software development so that computer technology may be utilized to aid in the analysis process. One of the most preferred types of software development is the object-oriented approach. Object-oriented technology is a technique of organizing the software around real world objects. An existing finite element software package which calculates the elastic flexural-torsional buckling loads of a plane frame was obtained from previous research. This program is refactored into an object-oriented design to improve the structure of the software and increase its flexibility. Several examples are presented to compare the results of the software package to existing solutions. These examples show that the program provides acceptable results when analyzing a beam-column or plane frame structure subjected to concentrated moments and concentrated, axial, and distributed loads.
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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) | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.008 | 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".