Paradiso, Massimo (2022) A methodological framework for the formulation of geometrically exact beam models. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | A methodological framework for the formulation of geometrically exact beam models |
| Autori: | Autore Email Paradiso, Massimo massimo.paradiso@unina.it |
| Data: | 11 Gennaio 2022 |
| Numero di pagine: | 318 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Strutture per l'Ingegneria e l'Architettura |
| Dottorato: | Ingegneria strutturale, geotecnica e rischio sismico |
| Ciclo di dottorato: | 33 |
| Coordinatore del Corso di dottorato: | nome email Rosati, Luciano rosati@unina.it |
| Tutor: | nome email Rosati, Luciano [non definito] Marmo, Francesco [non definito] |
| Data: | 11 Gennaio 2022 |
| Numero di pagine: | 318 |
| Parole chiave: | Nonlinear beam models; Geometrically exact approach; Lie group methods |
| Settori scientifico-disciplinari del MIUR: | Area 08 - Ingegneria civile e Architettura > ICAR/08 - Scienza delle costruzioni |
| Depositato il: | 02 Feb 2022 07:47 |
| Ultima modifica: | 07 Giu 2023 11:19 |
| URI: | http://www.fedoa.unina.it/id/eprint/13533 |
Abstract
The theme of high flexible beams has received growing attention during the last decades and, in parallel, a number of beam models have been proposed in the last half century based on several modeling strategies. Aim of this dissertation is to describe the mathematical fundamentals and outline a methodological framework for formulating geometrically exact models for the analysis of beams undergoing large displacements. The modeling approach followed is the geometrically exact one. Is is based on a reduction process deriving the beam kinematics from the exact deformation analysis of a solid body. The beam model is derived by constraining the three-dimensional solid with the introduction of specific kinematic assumptions. The formulation leads to conceive the beam in terms of a three-dimensional orthogonal moving frame, with one of its axis remaining orthogonal to the beam cross-section in any configuration. This moving frame is also the reference system at which the resultant force and torque, acting on the typical cross-section, are evaluated. The geometric description of the beam model leads to a characterization of the beam cross-section configuration as an affine transformation within the physical space. Then, the space of the spatial proper rigid motions is assumed as the configuration space and the beam model is formulated in terms of curves of the special Euclidean Lie group, namely SE(3).
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