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Numerical Methods in Continuum Mechanics 1

last update: 2017-03-29

[ 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 2, 201610:15 - 11:45 Room: K 009DLecture 1: Introduction
Thu, Mar 3, 201610:15 - 11:45 Room: K 001ALecture 2
Wed, Mar 9, 201610:15 - 11:45 Room: K 009DLecture 3
Thu, Mar 10, 201610:15 - 11:00 Room: K 001ALecture 4
Wed, Mar 16, 201610:15 - 11:45 Room: K 009DLecture 5
Easter Break
Wed, Apr 6, 201610:15 - 11:45 Room: K 009DLecture 6
Wed, Apr 13, 201610:15 - 11:45 Room: K 009DLecture 7
Wed, Apr 20, 201610:15 - 11:45 Room: K 009DLecture 8
Wed, Apr 27, 201610:15 - 11:45 Room: K 009DLecture 9
Wed, May 4, 2016Landespatron (no lecture)
Wed, May 11, 201610:15 - 11:45 Room: K 009DLecture 10
Wed, May 18, 201610:15 - 11:45 Room: K 009DLecture 11
Wed, May 25, 2016Canceled
Wed, Jun 1, 201610:15 - 11:45 Room: K 009DLecture 12
Wed, Jun 8, 201610:15 - 11:45 Room: K 009DLecture 13
Wed, Jun 15, 2016Canceled
Wed, Jun 22, 201610:15 - 11:45 Room: K 009DLecture 14
Wed, Jun 29, 201610:15 - 11:45 Room: K 009DLecture 15


- Prüfungsfragen: up
als   pdf-file  

- Prüfungstermine: up
Link zu Prüfungsterminen


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

Tutorials held by: O.Univ.-Prof. Dr. Ulrich Langer

Time and room:

Thu, Mar 17, 201610:15 - 11:00 Room: K 001ATutorial 01
Easter Break
Thu, Apr 7, 201610:15 - 11:00 Room: K 001ATutorial 02
Thu, Apr 14, 2016Canceled
Thu, Apr 21, 201610:15 - 11:45 Room: K 001ATutorial 03-04
Thu, Apr 28, 201610:15 - 11:00 Room: K 001ATutorial 05
Thu, May 5, 2016Holiday
Thu, May 12, 201610:15 - 11:45 Room: K 001ATutorial 06-07
Thu, May 19, 201610:15 - 11:00 Room: K 001ATutorial 08
Thu, May 26, 2016Holiday
Thu, Jun 2, 2016Canceled
Thu, Jun 9, 201610:15 - 11:00 Room: K 001ATutorial 09
Thu, Jun 16, 2016Canceled
Thu, Jun 23, 201610:15 - 11:45 Room: K 001ATutorial 10-11
Thu, Jun 30, 201610:15 - 11:00 Room: K 001ATutorial 12

Exercises
Exercises up
Tutorial 01Mar 17, 2016pdfTrace Spaces
Tutorial 02Apr 7, 2016pdf
Tutorial 03-04Apr 21, 2016pdf
Tutorial 05Apr 28, 2016pdf
Tutorial 06-07May 12, 2016pdf
Tutorial 08May 19, 2016pdf
Tutorial 09Jun 9, 2016pdf
Tutorial 10Jun 23, 2016pdf
Tutorial 11-12Jun 30, 2016pdf

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. PS-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.