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Geometric beam theory (GBT)
- Verantwortliche
- Dr. Rodrigo Takuro Sato Martin de Almagro, Prof. Dr.-Ing. habil. Sigrid Leyendecker
- Angaben
- Vorlesung mit Übung
Online 4 SWS, ECTS-Studium, ECTS-Credits: 5, Sprache Englisch, *The lectures will take place live via Zoom*
- Studienfächer / Studienrichtungen
- WF ME-BA-MG7 5-6 (ECTS-Credits: 5,0)
WF MB-BA ab 5 (ECTS-Credits: 5,0)
WF MB-BA-FG2 1-3 (ECTS-Credits: 5,0)
WF MB-MA-IP2 1 (ECTS-Credits: 5,0)
WF ME-MA-MG7 1-3 (ECTS-Credits: 5,0)
WF WING-MA 1-3 (ECTS-Credits: 5,0)
WF BPT-MA-M 3-4 (ECTS-Credits: 5,0)
- ECTS-Informationen:
- Title:
- Geometric beam theory
- Credits: 5
- Prerequisites
- Basic knowledge of dynamics and statics, elastostatics, linear algebra and some programming in Matlab.
Recommendations
Dynamik starrer Körper [DSK]
Statik und Festigkeitslehre [SuF]
Statik, Elastostatik und Festigkeitslehre [SEF]
Dynamik nichtlinearer Balken [DyNiLiBa]
Theoretische Dynamik [TheoDyn]
Numerische Methoden in der Mechanik [NuMeMech]
Description
In this course we aim to provide a theoretical overview of beam theory in the context of continuum mechanics and Lagrangian mechanics and its numerical treatment with an emphasis on geometry. We will introduce the concept of Lie group and their role in the description of the geometrically exact beam model used for large deformations.
- Contents
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- Literature
- R. Abraham and J. E. Marsden. Foundations of mechanics.
Javier Bonet and Richard D. Wood. Nonlinear continuum mechanics for finite element analysis.
R. Courant and D. Hilbert. Methods of mathematical physics. Vol. I.
Philippe G. Ciarlet. Mathematical elasticity. Studies in Mathematics and its Applications. Three-dimensional elasticity.
M. Fecko. Differential Geometry and Lie Groups for Physicists.
H. Goldstein, C.P. Poole, and J.L. Safko. Classical Mechanics.
D. D. Holm. Geometric mechanics. Part II. Rotating, translating and rolling.
J. Lemaitre and J. L. Chaboche. Mechanics of solid materials.
J. M. Lee. Introduction to Smooth Manifolds.
Julia Mergheim. Lecture notes - Nonlinear Finite Element Methods. July 2011.
Jerrold E. Marsden and Thomas J. R. Hughes. Mathematical foundations of elasticity.
Peter J. Olver. Applications of Lie groups to differential equations.
H.-R. Schwarz. Finite element methods.
J. Simo. A finite strain beam formulation. The three-dimensional dynamic problem. Part I.
- Zusätzliche Informationen
- Erwartete Teilnehmerzahl: 25, Maximale Teilnehmerzahl: 50
www: https://www.studon.fau.de/crs3245235.html Für diese Lehrveranstaltung ist eine Anmeldung erforderlich. Die Anmeldung erfolgt über: StudOn
- Verwendung in folgenden UnivIS-Modulen
- Startsemester WS 2020/2021:
- Geometric Beam Theory (GBT)
- Institution: Lehrstuhl für Technische Dynamik (LTD)
Kurse
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