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Numerical Methods in Continuum Mechanics 1

last update: 2021-10-03
[ Lecture ]  [ Tutorial ]  [ Exercises ]   [ Transparencies ]  [ Lecture Notes ]   [ Additional Literature ]   [ Software ]  [ Links ]  [ General ]   [ Home ]
Lecture
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(CourseId 327.005, 2 hours per week, Semester 6)

Lecturer: O.Univ.-Prof. Dr. Ulrich Langer

Time and room:

Wed, Mar 5, 200808:30 - 10:00 Room: T 111Lecture 1
Wed, Mar 12, 200808:30 - 10:00 Room: T 111Lecture 2
Easter Break
Wed, Apr 2, 200808:30 - 10:00 Room: T 111Lecture 3
Wed, Apr 9, 200808:30 - 10:00 Room: T 111Lecture 4
Wed, Apr 16, 200808:30 - 10:00 Room: T 111Lecture 5
Wed, Apr 23, 200808:30 - 10:00 Room: T 111Lecture 6
Wed, Apr 30, 200808:30 - 10:00 Room: T 111Lecture 7
Wed, May 7, 200808:30 - 10:00 Room: T 111Lecture 8
Wed, May 14, 200808:30 - 10:00 Room: T 111Lecture 9
Wed, May 21, 200808:30 - 10:00 Room: T 111Lecture 10
Wed, May 28, 200808:30 - 10:00 Room: T 111Lecture 11
Wed, Jun 4, 200808:30 - 10:00 Room: T 111Lecture 12
Wed, Jun 11, 200808:30 - 10:00 Room: T 111Lecture 13
Wed, Jun 18, 200808:30 - 10:00 Room: T 111Lecture 14
Wed, Jun 25, 200808:30 - 10:00 Room: T 111Lecture 15

Lecturer: O.Univ.-Prof. Dr. Ulrich Langer

Tutorial
Tutorial up

(CourseId 327.006, 1 hour per week, Semester 6)

Tutorials held by: DI Peter Gruber

Time and room:

Fri, Mar 7, 200808:30 - 09:15 Room: T 1010Introduction
Fri, Mar 14, 200808:30 - 09:15 Room: T 1010Tutorial 1
Easter Break
Fri, Apr 4, 200808:30 - 09:15 Room: T 1010Tutorial 2
Fri, Apr 11, 200808:30 - 09:15 Room: T 1010Tutorial 3
Fri, Apr 18, 200808:30 - 09:15 Room: T 1010Tutorial 4
Fri, Apr 25, 200808:30 - 09:15 Room: T 1010Tutorial 5
Fri, May 2, 200808:30 - 09:15 Room: T 1010Tutorial 6
Fri, May 9, 2008cancelled!
Fri, May 16, 200808:30 - 09:15 Room: T 1010Tutorial 7
Fri, May 16, 200809:15 - 10:00 Room: T 1010Tutorial 8
Fri, May 30, 200808:30 - 09:15 Room: T 1010Tutorial 9
Fri, Jun 6, 200808:30 - 09:15 Room: T 1010Tutorial 10
Fri, Jun 13, 200808:30 - 09:15 Room: T 1010Tutorial 11
Fri, Jun 20, 200808:30 - 09:15 Room: T 1010Tutorial 12
Fri, Jun 27, 200808:30 - 09:15 Room: T 1010Tutorial 13

Exercises
Exercises up
Tutorial 1Mar 14, 2008pdf
Tutorial 2Apr 4, 2008pdf
Tutorial 3Apr 11, 2008pdf
Tutorial 4Apr 18, 2008pdf
Tutorial 5Apr 25, 2008pdf
Tutorial 6May 2, 2008pdf
Tutorial 7May 16, 2008pdf
Tutorial 8May 16, 2008pdf
Tutorial 9May 30, 2008pdf
Tutorial 10June 6, 2008pdf
Tutorial 11June 13, 2008pdf
Tutorial 12June 20, 2008pdf
Tutorial 13June 27, 2008pdf

Transparencies
Transparencies up
Transparency 1: b/w1.1.1 Primal VF I
Transparency 2: b/w1.1.1 Primal VF II
Transparency 2a: colourExample 1.3: I
Transparency 2b: colourExample 1.3: II
Transparency 2c: colourTheorem 1.4
Transparency 3: b/wCorollaries 1.6/1.7
Transparency 4: b/w1.2.1 Nonlin. VP
Transparency 5: colour1.2.2 VI 1
Transparency 6: colour1.2.2 VI 2
Transparency 7: colour1.2.2 VI 3
Transparency 7a: colourProof: Existence
Transparency 7b: colourProof: Uniqueness+Nonexp.
Transparency 8: b/wRemark 2.1
Transparency 8a: colourExercises 2.3 and 2.5
Transparency 8b: colourLemma 2.8
Transparency 8c: colourProof
Transparency 8d: colourTheorem 2.9
Transparency 9: colour2.2 Sym. Case I
Transparency 10: colour2.2 Sym. Case II
Transparency 11: colour2.2 Sym. Case III
Transparency 12: b/w2.2 Sym. Case IV
Transparency 13: b/w2.2 Sym. Case V
Transparency 14: colour2.2 Sym. Case VI
Transparency 15: colour2.3 MVP(+) I
Transparency 16: b/w2.3 MVP(+) II
Transparency 17: b/w2.3 MVP(+) III
Transparency 18: colour2.3 MVP(+) IV
Transparency 19: colour2.4 Exercises
Transparency 20: colour2.4.2 Arrow-Hurwicz
Transparency 21: b/w2.4.3 Theorem 2.21
Transparency 22: b/w2.4.3 Proof I
Transparency 23: colour2.4.3 Proof II
Transparency 24: colour2.4.3 Proof III
Transparency 25: colour2.4.3 Example 2.22
Transparency 26: colour2.4.3 Preconditioner
Transparency 27: colour2.4.3 Excerises 2.24/25
Transparency 28: colour3.1. Basic equations
Transparency 29: colour3.2.1 Derivation PVF
Transparency 30: colour3.2.1 PVF=MP
Transparency 31: colour3.2.1 Ass. L&M
Transparency 32: b/w3.2.1 RBM
Transparency 33: b/w3.2.1 1st KORN
Transparency 34: b/w3.2.1 KORN's ineq.
Transparency 35: b/w3.2.1 2nd KORN
Transparency 36: b/w3.2.1 L&M
Transparency 37: b/w3.2.1 Exercise 3.8
Transparency 38: colour3.2.1 FEM
Transparency 39: colour3.2.2 HRP I 1
Transparency 40: b/w3.2.2 HRP I 2
Transparency 41: b/w3.2.2 HRP I 3
Transparency 42: colour3.2.2 HRP I 4
Transparency 43: colour3.2.2 HRP II MFEM
Transparency 44a: b/wPunkt 3.2.3. I
Transparency 44b: b/wPunkt 3.2.3. II
Transparency 44c: b/wPunkt 3.2.3. III
Transparency 44d: b/wPunkt 3.2.3. IV
Transparency 44e: b/wPunkt 3.2.3. V
Transparency 45: colourFE-Discr.
Transparency 46: colourFE-System
Lecture Notes
Basic Lecture Notes up
  1. Langer U.: Numerische Festkörpermechanik (Computational Mechanics), JKU, Linz 1997. pdf-File
  2. Zulehner W.: Lecture Notes for the Course Numerical Methods for Continuum Mechanics 1, JKU, Linz 2006. pdf-File
Additional Literature
Additional Literature up
  1. Braess D.: Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie. Springer Lehrbuch, Berlin, Heidelberg 1997, see also Braess' homepage
  2. Braess D.: Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 1997, 2001, 2007. (= english version of [1])
  3. Brezzi F., Fortin M.: Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics, Vol. 15, Springer-Verlag, New York 1991.
Software
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Links
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General
General Information up
Previous Knowledge: Is required for: Objective:

Get knowledge of analysis tools and of numerical methods for mechanical problems

Contents:
  1. Introduction
  2. Analysis and numerics of mixed boundary value problems
  3. Modelling, analysis and numerics of linear elasticity problems
  4. Structural mechanics
Additional Information: Examinations:

Lecture: oral
Tutorial: The mark of the tutorial consists of the assessment of the individual exercises and the presentations on the blackboard.