Nonlinear Finite Element Methods
Current information on the schedule of the lecture can be found at the OPAL page.
Dr.-Ing. habil. Geralf Hütter
- Engineering Mechanics
- Fundamental knowledge of FEM for linear-elastic problems (e. g. courses "Introduction to the Finite Element Method", "Numerische Methoden der Mechanik", "Einführung in die Methode der finiten Elemente" or MIT course, lectures 1 to 7 )
The course focuses on the application of the Finite Element Method (FEM) to nonlinear, time-dependent and coupled problems.
- Introduction and fundamentals
- Spatial discretization
- Galerkin's method
- Numerical Integration (Quadrature)
- Nonlinear elastic problems
- Newton-Raphson method in FEM
- Irreversible Material
- Runge-Kutta methods
- History-dependent material behavior
- Dynamic problems:
- explicit dynamics
- FEM for large deformations
- FEM for thermomechanical problems
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).
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.
- Bathe: “Finite Element Procedures” / "Finite-Elemente-Methoden" (Hardcopy avalaible in the library of TU BAF, e-book at mit.edu)
- Belytschko, Liu, Moran: "Nonlinear Finite Elements for Continua and Structures", Hardcopy avalaible in the library of TU BAF
- 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)
- Reddy: An introduction to nonlinear finite element analysis (Hardcopy avalaible in the library)
- Wriggers: "Nonlinear Finite Element Methods" / "Nichtlineare Finite-Element-Methoden" (Hardcopy and E-Book avalaible in the library of TU BAF)
- 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
|Lecture||Thursday||09:15 – 10:45||WEI-1051||Dr. G. Hütter|
|Exercise 1 (German)||Friday, even weeks||09:15 – 10:45||WEI-0120||Dr. G. Hütter|
|Exercise 2 (English)||Tuesday, even weeks||11:00 – 12:30||WEI-1051||M.Sc. J. Abraham|
|Computer exercise 1 (German)||Friday, odd weeks||09:15 – 10:45||WEI-1218||Dr. G. Hütter|
|Computer exercise 2 (German)||Tuesday, odd weeks||11:00 – 12:30||WEI-1218a||M.Sc. J. Abraham|
Note: The first exercise takes place at 2nd of April!
Detailed schedule including plan for exercises
|semester week||KW / calender week|
Exercise 1 (German)
(Friday, WEI-120 / 1218)
Exercise 2 (English)
(Tuesday, WEI-1051 / 1218a)
|1||14||04/04/2019||Ex 2.1: Wiederholung lineare FEM für Stab||Ex 2.1: Revision linear FEM for Rods|
Ex 3.1-3.3: Schwache Form/Galerkin
|Ex 1.1-1.2: Algorithms in MatLab/Python|
|3||16||18/04/2019||Karfreitag||Ex 3.1-3.3: Weak form/Galerkin method|
|4||17||25/04/2019||Ex 1.1-1.2: Algorithmen in MatLab/Python||Ex 2.2: 1D FEM inMatlab/Python|
|5||18||02/05/2019||Ex 4.3, 4.4, 4.2: Formfunktionen||Ex 4.3, 4.4, 4.2: Shape functions|
|6||19||09/05/2019||Ex 2.2: 1D-FEM in Matlab/Python||Introduction to Abaqus|
|7||20||16/05/2019||Ex 5.1-5.2: Gauß-Integration||Ex 5.1-5.2: Gauss integration|
|8||21||23/05/2019||Ex 5.3: Gauß-Integration||Ex 5.3: Gauss integration|
Ex 6.1-6.2: Newton-Verfahren
|Ex 6.1-6.2: Newton method|
|Ex 6.3: Newton-Verfahren||Ex 6.3: Newton method|
|Ex 7.1: Zeitntegration||Ex 7.1: Time integration|
|Ex 7.2: Zeitntegration||Ex 7.2: Time integration|
|Konsultation zum Beleg||consultation hour for assigment|
|Ex 7.3: Newmark-Verfahren||Ex 7.3: Newmark-Verfahren|
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.