Nonlinear Finite Element Methods

Current information on the schedule of the lecture can be found at the OPAL page.

Lecture

Dr.-Ing. habil. Geralf Hütter

Requirements

Contents

The course focuses on the application of the Finite Element Method (FEM) to nonlinear, time-dependent and coupled  problems.

  1. Introduction and fundamentals
  2. Spatial discretization
    1. Galerkin's method
    2. Elements
    3. Numerical Integration (Quadrature)
  3. Nonlinear elastic problems
    1. Newton-Raphson method in FEM
  4. Irreversible Material
    1. Runge-Kutta methods
    2. History-dependent material behavior
  5. Dynamic problems:
    1. Newmark-method
    2. explicit dynamics
  6. FEM for large deformations
  7. FEM for thermomechanical problems

Examination

Written examination

The written examination consists of two parts. A question part which has to be done without any auxilary material, and a part "tasks" for which two hand-written sheets of paper (DIN A4, double-sided, no complete exercise solutions) , a mathematical formulary and a pocket calculator (without algebra system) may be used. Usage of any other electronic devices during examination is not allowed.

Successful completion of the assignment is mandatory for taking the examination (Prüfungsvorleistung - PVL). 

Assignment

The task for the assignment in summer term will be published during the semester.

The students are encouraged to ask questions on the assignment asked after the lecture or during exercises and computer practices.

Further Readings:

  1. Bathe: “Finite Element Procedures” / "Finite-Elemente-Methoden" (Hardcopy avalaible in the library of TU BAF, e-book at mit.edu)
  2. Belytschko, Liu, Moran: "Nonlinear Finite Elements for Continua and Structures",  Hardcopy avalaible in the library of TU BAF
  3. de Borst, Crisfield, Remmers, Verhoosel: "Non‐Linear Finite Element Analysis of Solids and Structures" / " Nichtlineare Finite-Elemente-Analyse von Festkörpern und Strukturen"  (Hardcopy and E-Book avalaible in the library of TU BAF)
  4. Reddy: An introduction to nonlinear finite element analysis (Hardcopy avalaible in the library)
  5. Wriggers: "Nonlinear Finite Element Methods" / "Nichtlineare Finite-Element-Methoden" (Hardcopy and E-Book avalaible in the library of TU BAF)
  6. Zienkiewicz, Taylor: "Finite Element Method"/"Methode der finiten Elemente", Volumes 1 and 2 (Hardcopy and E-Book avalaible in the library of TU BAF)

Schedule for summer term 2019

LectureThursday09:15 – 10:45WEI-1051Dr. G. Hütter
Exercise 1 (German)Friday, even weeks09:15 – 10:45WEI-0120
Dr. G. Hütter
Exercise 2 (English)Tuesday, even weeks11:00 12:30WEI-1051M.Sc. J. Abraham
Computer exercise 1 (German)
Friday, odd weeks09:15 – 10:45WEI-1218
Dr. G. Hütter
Computer exercise 2 (German)Tuesday, odd weeks11:00 12:30WEI-1218aM.Sc. J. Abraham

Note: The first exercise takes place at 2nd of April!

Detailed schedule including plan for exercises

semester weekKW / calender week

Lecture

(Thursday)

Exercise 1 (German)

(Friday, WEI-120 / 1218)

Exercise 2 (English)

(Tuesday, WEI-1051 / 1218a)

11404/04/2019Ex 2.1: Wiederholung lineare FEM für Stab
Ex 2.1: Revision linear FEM for Rods
21511/04/2019

Ex 3.1-3.3: Schwache Form/Galerkin

(WEI-120)

Ex 1.1-1.2: Algorithms in MatLab/Python
31618/04/2019KarfreitagEx 3.1-3.3: Weak form/Galerkin method
41725/04/2019Ex 1.1-1.2: Algorithmen in MatLab/PythonEx 2.2: 1D FEM inMatlab/Python
51802/05/2019Ex 4.3, 4.4, 4.2: FormfunktionenEx 4.3, 4.4, 4.2: Shape functions
61909/05/2019Ex 2.2: 1D-FEM in Matlab/PythonIntroduction to Abaqus
72016/05/2019Ex 5.1-5.2: Gauß-IntegrationEx 5.1-5.2: Gauss integration
82123/05/2019Ex 5.3: Gauß-IntegrationEx 5.3: Gauss integration
922

No lecture!

30/05/2019

(Christi Himmelfahrt))

Ex 6.1-6.2: Newton-Verfahren

(28.05.2019, 09:15-11:00)

Ex 6.1-6.2: Newton method
1023

06/06/2019

(room: LAM-1213)

Ex 6.3: Newton-VerfahrenEx 6.3: Newton method
1124

No lecture!

13/06/2019

Download: Mises-plasticity

Ex 7.1: ZeitntegrationEx 7.1: Time integration
1225

20/06/2019

Ex 7.2: ZeitntegrationEx 7.2: Time integration
1326

27/06/2019

Download: Stability Analysis for Explicit Dynamic FEM

Konsultation zum Belegconsultation hour for assigment
1427

04/07/2018

Ex 7.3: Newmark-VerfahrenEx 7.3: Newmark-Verfahren
1528

11/07/2018

Download: Summary

Ex 4.5: Äußere Last

Ex 4.5: External load

The task numbers like "Ex 1.1" refer to the exercise book which will be provided as hardcopy in the first lecture.