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Methode der Finiten Elemente II (18/1)

Finite Element Methods II (18/1)

Announcements

The grades of the FEM exams can be viewed on the notice board (right next to the elevator) at our institute.

The post­-exam review for the written exam and the assignments will take place on Friday, 19.10.2018 at 14.00 in room 165, MB1.


Contents

Nowadays, the Finite Element Method (FEM) represents one of most widespread calculation methods in modern engineering. It helps even the way of looking at problems regarding different physical-technical procedures. The concept of Finite Element Method consists of a numerical procedure for the approximate solution of linear and non-linear (initial) boundary value problems which are typically formulated through partial differential equations.

The lectures focus on the following subjects:

  • Dynamics, transient problems, time integration, eigen-frequencies, eigen-modes
  • Nonlinear and time-dependent material models (elasto-plasticity and visco-elasticity)
  • Special elements for quasi-incompressible problems




Lectures

 

Semester Lecturer Date Location

Summer 2018

Dr.-Ing. Patrick Kurzeja

Tuesday, 11:30 - 13:00

Start: April 10, 2018

MB-I building - E-21

Date

Location

Description

10.04.2018

MB-I building E-21

introduction
weak form

17.04.2018

MB-I building E-21

weak form (contd.)
oscillation eigenmodes
mass matrix

24.04.2018

MB-I building E-21

mass matrix (examples)
central difference method

03.05.2018
(12:15-13:45)

MB-I building
165

Newmark method
non-linear systems (Newton-Raphson)

08.05.2018

MB-I building E-21

numerical integration of ode (Backward-Euler)
linear viscoelasticity
standard rheological model of a linear viscoelastic material

15.05.2018

MB-I building E21

exercise instead of lecture

22.05.2018

MB-I building E21

standard rheological model of a linear viscoelastic material (contd.)
elasto-plasticity in 1D (rheological model)

29.05.2018

MB-I building E21

elasto-plasticity in 1D (Coleman & Noll approach,
Karush-Kuhn-Tucker conditions,
predictor-corrector scheme,
loading-unloading cycle)

05.06.2018

MB-I building E21

elasto-plasticity in 1D (loading-unloading cycle),
hardening,
linear isotropic hardening,

12.06.2018

MB-263 CIP-Pool

exercise instead of lecture

19.06.2018

MB-I building E21 hardening,
linear isotropic hardening (contd.)

26.06.2018

MB-I building E21 linear kinematic hardening
exponential saturation-type hardening

03.07.2018

MB-I building E21 exponential saturation-type hardening (contd.)
thermodynamics of the hardening process
non-linear behaviour in 1D

10.07.2018

MB-I building E21 non-linear behaviour in 1D
non-linear behaviour in 3D

17.07.2018

MB-I building E21 non-linear behaviour in 3D

19.07.2018

MB-I building room 165 simulation of incompressible materials

Lecture notes

latest version (19.07.2018 - complete)


Tutorials

 

Semester

Supervisor

Date

Location

Summer 2018

Lars Rose, M.Sc.

Serhat Aygün, M.Sc.

Thursday, 12:15 - 14:00

Start: April 12, 2018

MB-I building, Room 263 (CIP-Pool)

 

Accompanying documents for the tutorials

The documents accompanying the tutorials are to be used in preparation of each exercise. All participants are requested to become acquainted with the exercises dealing with the subject of the respective tutorial. This will ensure that all participants are on the same level of knowledge for each individual lesson.

 

Tutorial No.

Date

Location

Description

Files

1

12.04.2018

MB-263 CIP-Pool

Pre- and Post-processing with GiD

Tutorial 01
FEM routine
GiD data
Geometry - Plate
Solution 01

2

19.04.2018

MB-263 CIP-Pool

Determination of global mass matrix

Tutorial 02
plot routine
3

26.04.2018

MB-263 CIP-Pool

Central Difference Method

Tutorial 03

4

17.05.2018

MB-263 CIP-Pool

Newmark Method

Tutorial 04

5

24.05.2018

MB-263 CIP-Pool

Comparison CDM & Newmark Tutorial 05
Geometry - Beam

6

07.06.2018

MB-263 CIP-Pool

Two dimensional truss structures

(based on solution of Tutorial 1)

Tutorial 06
Geometry - Truss
GiD data

7

12.06.2018

MB-263 CIP-Pool

Two dimensional truss structures (continued)

8

14.06.2018

MB-263 CIP-Pool

Nonlinear FEM - the residual format

Tutorial 08

9

21.06.2018

MB-263 CIP-Pool

One-Dimensional linear viscoelastic model

Tutorial 09

10

28.06.2018

MB-263 CIP-Pool

One-Dimensional perfect elastoplastic model

Tutorial 10
11 05.07.2018 MB-263 CIP-Pool

One-Dimensional elastoplastic model with linear isotropic hardening

Tutorial 11
12 12.07.2018 MB-263 CIP-Pool

One-Dimensional elastoplastic model with

non-linear hardening law

Tutorial 12
19.07.2018 MB-I building room 165

lecture instead of exercise

Tutorials 8-12 are each based on the solution of the previous tutorial.

 


Assignment

For the MMT-students it is obligatory and highly recommended for the other students. Please contact your tutorial supervisor (Lars Rose) in advance and register with your name and immatriculation number.

 

Homework
No.
Description Additional
Information
Date of
Submission

1

Elastoplatic response of a truss structure

deadline for registration is
20.07.2018

07.09.2018




Examination

For the exam, a registration via the BOSS-System in NOT REQUIRED.

Please register  via e-mail to Lars Rose (include your immatriculation number) until 07.09.2018.

The examination will take place on Friday, 21.09.18 from 11:00 - 13:00 in room HG2, HS6.

Note:

  • The examination consists of two parts, theoretical and numerical
  • NO auxiliaries (scripts, lecture notes, exercise sheets, etc.) are allowed for either part
  • Please bring your scientific calculator

Exercises for exam preparation


Literature

German literature:
P. Wriggers: Nichtlineare Finite-Element-Methoden, Springer, 2001.

English literature:
J.N. Reddy: An Introduction to the Finite Element Method, McGraw-Hill, 2006.
J.C. Simo, T.J.R. Hughes: Computational Inelasticity, Springer, 1998.
T.J.R. Hughes: The Finite Element Method, Prentice Hall, 1987.
K.-J. Bathe: Finite Element Procedures, Prentice Hall, 1996.