Module Handbook

  • Dynamischer Default-Fachbereich geändert auf PHY

Notes on the module handbook of the department Physics

Die hier dargestellten Studiengang-, Modul- und Kursdaten des Fachbereichs Physik [PHY] befinden sich noch in Entwicklung und sind nicht offiziell.

Die offiziellen Modulhandbücher finden Sie unter https://www.physik.uni-kl.de/studium/modulhandbuecher/ .

Module PHY-SP-4-M-7

Schwerpunktmodul Technische Mechanik (M, 16.0 LP)

Module Identification

Module Number Module Name CP (Effort)
PHY-SP-4-M-7 Schwerpunktmodul Technische Mechanik 16.0 CP (480 h)

Basedata

CP, Effort 16.0 CP = 480 h
Position of the semester 2 Sem. from WiSe/SuSe
Level [7] Master (Advanced)
Language [DE] German
Module Manager
Lecturers
Area of study [PHY-TECHNO] TechnoPhysics
Reference course of study [PHY-88.B90-SG] M.Sc. TechnoPhysics
Livecycle-State [NORM] Active

Courses

Lehrveranstaltungen im Umfang von mindestens 16 LP aus folgendem Lehrveranstaltungsangebot (je nach Angebot):
Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
3V+1U MV-TM-86005-K-4
Continuum Mechanics
WP 56 h 124 h - - see comments 6.0 WiSe
3V+1U MV-TM-86012-K-4
Finite Elements
WP 56 h 124 h - - see comments 6.0 SuSe
2V+1U MV-TM-86004-K-4
Engineering Mechanics IV
WP 42 h 78 h - - see comments 4.0 SuSe
2V+2U MV-TM-86013-K-4
Non-linear Finite Elements
WP 56 h 124 h - - see comments 6.0 WiSe
2V MV-TM-86006-K-7
Non-linear Continuum Mechanics
WP 28 h 62 h - - see comments 3.0 SuSe
2V MV-TM-86010-K-4
Selected Topics of Mechanics
WP 28 h 62 h - - see comments 3.0 SuSe
2V MV-TM-86026-K-4
Contact Mechanics
WP 28 h 62 h - - see comments 3.0 WiSe
2V MV-TM-86008-K-7
Fracture mechanics
WP 28 h 62 h - - see comments 3.0 SuSe
2V MV-LTM-86009-K-7
Engineering Optimization
P 28 h 62 h - - see comments 3.0 SuSe
  • About [MV-TM-86005-K-4]: Title: "Continuum Mechanics"; Presence-Time: 56 h; Self-Study: 124 h
  • About [MV-TM-86012-K-4]: Title: "Finite Elements"; Presence-Time: 56 h; Self-Study: 124 h
  • About [MV-TM-86004-K-4]: Title: "Engineering Mechanics IV"; Presence-Time: 42 h; Self-Study: 78 h
  • About [MV-TM-86013-K-4]: Title: "Non-linear Finite Elements"; Presence-Time: 56 h; Self-Study: 124 h
  • About [MV-TM-86006-K-7]: Title: "Non-linear Continuum Mechanics"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MV-TM-86010-K-4]: Title: "Selected Topics of Mechanics"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MV-TM-86026-K-4]: Title: "Contact Mechanics"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MV-TM-86008-K-7]: Title: "Fracture mechanics"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MV-LTM-86009-K-7]: Title: "Engineering Optimization"; Presence-Time: 28 h; Self-Study: 62 h
Some of the courses take place at irregular intervals. A current overview of the courses offered can be found in the campus management system of the TU Kaiserslautern (https://www.kis.uni-kl.de).

Note on credits, test performances and examinations:

The lecturers determine the credits, test performances and examinations. The examination modalities follow the practices of the respective oganizing department or institution.

Students are strongly advised to inform themselves at the respective lecturers at the beginning of the course.

Evaluation of grades

All partial module examinations have to be passed. The module grade is the arithmetic mean of all partial examination grades.


Contents

  • Basic concepts of (linear) continuum mechanics
  • Stress and Equilibrium
  • Deformation and Strains
  • Material Behaviour (Linear Elastic Solid)
  • Two-Dimensional Problems (Plane Strain / Plane Stress / Airy Stress Function / Problem Solution)
  • Plate Theory
  • Three-Dimensional Problems
  • Variational Principles and Energy Methods
  • Principles of the numerical solution for boundary value problems (weighted residuals, collocation and Ritz methods for trusses and beams)
  • One-dimensional discretization with the Finite Element Method (FEM)
  • Element technology for one- and two-dimensional problems (shape functions, numerical integration, isoparametric concept).
  • Assembly of the global equation system (element stiffness matrix, element residuals)
  • Truss and beam elements
  • Displacement and mixed-formulation based elements for plane elasticity problems
  • fundamentals of oscillations
  • free and driven oscillations with and without damping (amplitude and phase response)
  • Lagrange equations of the second kind (one and two degrees of freedom, resonance, tuned mass damper)
  • continuum oscillations (string, normal strain and torsion bars, beams, wave propagation, solutions of d’Alembert and Bernoulli)
  • Non-linear phenomena in mechanics
  • Continuum description of elastic materials at finite deformations
  • The weak form of equilibrium in the reference configuration as well as in the current configuration
  • Linearization
  • Isoparametric concept
  • Discretization in the reference configuration as well as in the current configuration
  • Implementation of Von-Mises plasticity at small strains
  • Time integration of internal variables
  • Iterative solution strategies for time-independent, non-linear problems
Kinematics
  • Deformation
  • Time-derivatives
  • Strain
  • Objectivity

Balance laws

  • Reynold‘s theorem
  • General form of a balance law
  • Balance of mass
  • Balance of linear momentum
  • Balance of angular momentum
  • Balance of energy and entropy
  • Second law of thermodynamics

Constitutive Laws

  • General form
  • Simplifications
  • Thermo-elastic and hyperelastic materials
  • Fluids
In the lecture, partial aspects of mechanics are taught which cannot be taught in the basic lectures. The mathematical basics of tensor calculation in curvilinear coordinates are dealt with. The concepts are applied in shell theory, micromechanics and plasticity theory.
  • Introduction to Tensor Calculus and Shell Theory
    • Euclidean vector space
    • covariant and contravariant coordinates
    • vector and tensor algebra in curvilinear coordinates
    • covariant derivatives, vector and tensor analysis
    • membrane and bending theory for shells
  • Micro Mechanics
    • Eshelby solution for inclusions and inhomogeneities
    • analytical homogenization
  • Theory of Plasticity
    • fundamentals of plastic deformation
    • von Mises, Tresca, and Mohr yield surfaces
    • associated and not associated flow rules
    • rate dependent and rate independent plasticity
  • Kinematic and static contact conditions
  • Hertz-Signorini-Moreau condition, Karush-Kuhn-Tucker condition
  • Hertzian contact theory
  • Friction laws
  • Signorini problem for infinitesimal deformations
  • Variational inequalities for contact problems
  • Existence and uniqueness of solutions
  • Finite element discretization
  • Solution of discrete variational inequalities (penalty method, method of Lagrangian multipliers, relaxation method with projection)
  • Dynamic contact problems with friction
  • purpose, assumptions, and development of fracture mechanics
  • fundamentals of the theory of elasticity
  • notch problems with different notch shapes
  • crack problems
  • asymptotic approach
  • intensity concepts
  • energetic approach
  • mixed-mode fracture mechanics
  • elasto-plastic fracture mechanics
  • plastic fracture mechanics
  • fracture resistance curve
The basic concepts and fundamental quantities of mathematical optimization are presented, in which a focus is put on aspects which are of foremost importance for structural optimization problems. As part of an introduction, basic knowledge of mathematical terms and aspects of optimization is imparted. Afterwards optimization problems without constraints as well as problems with constraints are considered. Based on this, alternative formulations of an optimization problem (so-called Lagrange duality) are presented with the help of Lagrange functions. Subsequently approximation methods, optimality criteria methods and multi-criteria optimization are considered. Finally, outlooks on other areas such as shape optimization and topology optimization are given.

Competencies / intended learning achievements

Die erfolgreiche Absolvierung dieses Moduls führt zu folgenden Kenntnissen & Fertigkeiten (als Lernergebnisse) und Kompetenzen:
  • Struktur und Dynamik mechanischer Systeme soweit zu verstehen, dass die gelehrten Methoden und Denkweisen auf Fragestellungen aus diesem Bereich angewendet werden können.
  • ein strukturiertes Fachwissen (Verfügungswissen) zu den Teilgebieten und Themen der technischen Mechanik, die inhaltlicher Gegenstand der oben genannten Lehrveranstaltungen dieses Vertiefungsmoduls sind (Fachkompetenz)
  • das Verständnis des Zusammenwirkens von theoretischen Betrachtungen und praktischer Handhabung von Mechanik
  • ein Überblickswissen (Orientierungswissen) zu den aktuellen, grundlegenden Fragestellungen der technischen Mechanik (Fachkompetenz)
  • das Verständnis der Abweichungen von theoretischen Vorhersagen und experimentellen Ergebnissen
  • die Vertrautheit mit den Erkenntnismethoden, speziell bezogen auf die technische Mechanik und Erfahrungen in der exemplarischen Anwendung dieser Methoden in der Ingenieurwissenschaft (Methodenkompetenz)
  • die Vertrautheit mit den Arbeitsmethoden, speziell bezogen auf die technische Mechanik und Erfahrungen in der exemplarischen Anwendung dieser Methoden in der Ingenieurwissenschaft (Methodenkompetenz)
  • die Beherrschung der wichtigsten Arbeitsstrategien und Denkformen und damit auch die Vertrautheit mit den Strategien, Probleme der technischen Mechanik selbstständig zu identifizieren, zu strukturieren und systematisch zu lösen (Methoden- & Selbstkompetenz)

Literature

  • Becker, Gross: Mechanik elastischer Körper und Strukturen, Springer
  • Eschenauer, Schnell: Elastizitätstheorie I, B.I. Wissenschaftsverlag
  • Gurtin: The linear theory of elasticity, Truesdell, Clifford A.
  • Holzapfel: Nonlinear Solid Mechanics – A Continuum Approach for Engineering, Wiley
  • Kienzler, Schröder: Einführung in die Höhere Festigkeitslehre, Springer
  • Fung Tong: Classical and Computational Solid Mechanics, World Scientific
  • R. Ogden: Non-linear elastic deformations, Dover Publications 1984
  • Gross, Hauger, Wriggers: Technische Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
  • Gross, Hauger, Schröder, Werner: Formeln und Aufgaben zur Technischen Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
  • Wriggers: Nichtlineare Finite-Element-Methoden, Springer
  • Silber, Steinwender: Bauteilberechnung und Optimierung mit der FEM
  • Bathe: Finite Element Methoden, Springer
  • Hughes: The Finite Element Method, Prentice Hall
  • Zienkiewicz, Taylor: The Finite Element Method: The Basis, Butterworth-Heinemann
  • Zienkiewicz, Taylor: The Finite Element Method: Solid Mechanics, Butterworth­Heinemann
  • Gross, Hauger, Schröder, Wall: Technische Mechanik 3 – Kinetik, Springer
  • Gross, Ehlers, Wriggers, Schröder, Müller: Formeln und Aufgaben zur Technischen Mechanik 3 – Kinetik, Hydrodynamik, Springer
  • Hagedorn: Technische Mechanik 3 – Dynamik, Verlag Harri Deutsch
  • Gross, Hauger, Wriggers: Technische Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
  • Gross, Hauger, Schröder, Werner: Formeln und Aufgaben zur Technischen Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
  • Bathe: Finite Element Methoden, Springer
  • Belytschko, Liu, Moran: Nonlinear Finite Elements for Continua and Structures, Wiley 2000
  • Crisfield: The Finite Element Method - Non-linear Finite Element Analysis of Solids and Structures, Wiley 1991
  • Hughes: The Finite Element Method, Prentice Hall
  • Wriggers: Nichtlineare Finite-Element-Methoden, Springer
  • Zienkiewicz, Taylor: The Finite Element Method: The Basis, Butterworth-Heinemann
  • Zienkiewicz, Taylor: The Finite Element Method: Solid Mechanics, Butterworth-Heinemann
  • W. Becker, D. Gross; Mechanik elastischer Körper und Strukturen; Springer Berlin; ISBN: 3-540-43511-5
  • R. Kienzler, R. Schröder; Einführung in die Höhere Festigkeitslehre; Springer Berlin; ISBN: 3-540-89324-5
  • L. E. Malvern; Introduction to the Mechanics of a Continuous Medium; Prentice Hall; ISBN: 0-134-87603-0
  • R. W. Ogden; Non-Linear Elastic Deformations; Dover Pubn Inc; ISBN-10: 0-486-69648-0
  • P. Haupt; Continuum Mechanics and Theory of Materials; Springer Berlin; ISBN: 3-540-43111-X
  • R. Greve; Kontinuumsmechanik: Ein Grundkurs für Ingenieure und Physiker; Springer; ISBN: 3-540-00760-1
  • Y. C. Fung, P. Tong; Classical and Computational Solid Mechanics; World Scientific Publishing Company; ISBN-10: 9-810-24124-0
  • G. A. Holzapfel; Nonlinear Solid Mechanics: A Continuum Approach for Engineering; Wiley; ISBN-10: 0-471-82319-8
  • Altenbach, H. Altenbach; Einführung in die Kontinuumsmechanik; Teubner Studeinbücher Mechanik; ISBN: 3-519-03096-9
  • A.J.M. Spencer; Continuum Mechanics; Dover New York; ISBN 0-486-43594-6
  • M.E. Gurtin; An Introduction to Continuum Mechanics; Academic Press San Diego; ISBN: 0-12-309750-9
  • I-S. Liu; Continuum Mechanics; Springer Berlin; ISBN: 3-540-43019-9
  • E. Klingbeil: Tensorrechnung für Ingenieure, B.I.-Hochschultaschenbuch
  • D. Gross, Th. Seelig: Bruchmechanik - Mit einer Einführung in die Mikromechanik, Springer
  • N. Kikuchi u. J.T. Oden: Contact Problems in Elasticity, SIAM Philadelphia 1988
  • P. Wriggers: Computational Contact Mechanics, J. Wiley, New York 2002
  • K. Willner: Kontinuums- u. Kontaktmechanik, Springer, Berlin 2003
  • T.A. Laursen: Computational Contact and Impact Mechanics, Springer, Berlin, 2003
  • Gross, Seelig: Bruchmechanik – Mit einer Einführung in die Mikromechanik, Springer Verlag
  • Kienzler: Konzepte der Bruchmechanik, Vieweg
  • Kanninen, Popelar: Advanced Fracture Mechanics, Oxford Engineering Science Series
  • Harzheimer, L.: Strukturoptimierung - Grundlagen und Anwendungen, Verlag Harri Deutsch 2008
  • Spellucci, P.: Numerische Verfahren der nichtlinearen Optimierung, Birkhäuser Verlag 1993
  • Reinhard, R.; Hoffmann, A.; Gerlach T.: Nichtlineare Optimierung, Springer Verlag 2013
  • Schumacher, A.: Optimierung mechanischer Strukturen - Grundlagen und industrielle Anwendungen, Springer-Verlag 2005

Materials

depending on choice, see respective course description

Registration

depending on choice, see respective course description

Requirements for attendance (informal)

depending on choice, see respective course description

Requirements for attendance (formal)

None

References to Module / Module Number [PHY-SP-4-M-7]

Module-Pool Name
[PHY-SP-MV-MPOOL-7] Schwerpunktmodule aus dem Bereich Maschinenbau und Verfahrenstechnik: