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Modul: Modellbildung in der Festigkeitslehre [bauiM1S40-MODFEST]‌

Verantwortliche: P. Betsch

Studiengang: Bauingenieurwesen (M.Sc.)

Fach: Studienschwerpunkt "Konstruktiver Ingenieurbau" (SP 1)

Qualifikationsziele

(nicht übersetzt)

The goal of the course is to study various numerical analysis of engineering structures based on geometrical models of different dimensionality bars, beams, shells and solids. All finite element models are described from the geometrical point of view together with corresponding hypothesis of deformation. This allows to observe the continuous transformation of models and their geometrical model reductions from 3D continuum to the shell, beams and bar models. This process is illustrated by a corresponding set of finite elements available for the finite element analysis engineer.

Various types of the analysis depending on the engineering needs are studied: statical analysis including a- posteriori error analysis and mesh refinement; model analysis and its applications; buckling analysis in linear and non-linear descriptions; dynamic analysis in implicit and explicit formulations; harmonic analysis in application to the resonance phenomena.

All models are illustrated with FEM software, including practical programming in ANSYS APDL.

Erfolgskontrolle, gemäß SPO Bauingenieurwesen (M.Sc.)

Bildung der Modulnote

Modulnote ist Note der Prüfung

Bedingungen

darf nicht zusammen mit dem Modul Modellbildung in der Festigkeitslehre und Kinetische Stabilitätstheorie [bauiM1S34-MOFEKIST] gewählt werden.

Empfehlungen

Kurs Einführung in die Kontinuumsmechanik (6200607), Modul Grundlagen der Finiten Elemente [bauiM1S20- GRUNDFE]

Lehrveranstaltungen im Modul

Nr. Lehrveranstaltung LV-Typ SWS Sem. Lehrveranstaltungs- verantwortliche

6215807 Modellbildung in der Festigkeitslehre V/Ü 4 S A. Konyukhov

Arbeitsaufwand

Präsenzzeit (1 SWS = 1 Std. x 15 Wo.):

Vorlesung, Übung: 60 Std.

Selbststudium:

Vor- und Nachbereitung, Prüfungsvorbereitung: 120 Std. Summe: 180 Std.

Inhalt

(nicht übersetzt)

Description of objects in differential geometry: curves, surfaces, special selection of curvilinear coordinate system

Bauingenieurwesen (M.Sc.)

Modulhandbuch mit Stand 27.09.2016 104

4 MODULE 4.1 Module Studienschwerpunkt 1: Konstruktiver Ingenieurbau

for solid bodies. Various models of continuum mechanics based on specific geometry.

• 1D based models based on the geometry of curves - bars, chains, curvilinear beams. Kinematics of deformati- on, forces and moments, necessary boundary conditions. Sequence of mechanical models - chains, Bernoulli beams, Timoshenko beams - relationships with 3D models.

• 2D based models based on the geometry of surfaces - membranes, shells, solid-shells. Kinematics of defor- mation, membrane and moment stress-states.

Sequence of mechanical models - membrane, Kirchoff shells, Timoshenko shells, solid-shells and possibility of transversial deformations.

Necessary (Dirichlet) and essential (Neumann) boundary conditions. Relationships with 3D models.

• Special selection of a curvilinear coordinate system for a specific geometry of 3D bodies: cylindrical, spherical, spiral etc.

Various types of structural analysis:

• statical analysis for selected system;

• statical analysis for the sequence of the geometrical models 1D-2D-3D, mesh refinement, convergence and a-posteriori error analysis;

• modal analysis and its application to the resonance analysis;

• modal analysis and its application and its application to the mesh analysis as well as to the kinematic analysis of the system;

• buckling analysis in linear and non-linear formulations;

• transient analysis: implicit and explicit. Selection of the time integration step;

• harmonical analysis in application to the resonance phenomena.

Anmerkungen

Literature:

1. P. Wriggers, Nichtlineare Finite-Element-Methoden, Springer, 508 p., 2008.

2. P. Wriggers, Nonlinear Finite Element Methods, Springer, 560 p., 2008.

3. O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, The Finite Element Method. Its Basis and Fundamentals, ITS Basis and Fundamentals, Elsevier Ltd, Oxford; Auflage: 6th ed. 752 p., 2005.

4. Thomas J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Civil and Mechanical Engineering publication, 672 p., 2000.

5. T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, Wiley, 300 p., 2000.

6. http://www.ansys.com/Support/Documentation

7. http://www.lstc.com/download/manuals

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4 MODULE 4.2 Module Studienschwerpunkt 2: Wasser und Umwelt

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