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Methode der Finiten Elemente II (18/1)

Finite Element Methods II (18/1)

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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 2019

Jun. Prof. Dr.-Ing. habil. Sandra Klinge

Tuesday, 11:30 - 13:00

Start: April 02, 2019

MB-I building - E-21

Lecture No.

Description

1

introduction
weak form

2

weak form (contd.)
oscillation eigenmodes
mass matrix

3

mass matrix (examples)
central difference method

4

Newmark method
non-linear systems (Newton-Raphson)

5

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

6

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

7

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

8

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

9

hardening,
linear isotropic hardening (contd.)

10

linear kinematic hardening
exponential saturation-type hardening

11

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

12

non-linear behaviour in 1D
non-linear behaviour in 3D

13

non-linear behaviour in 3D

14

simulation of incompressible materials


Tutorials

 

Semester

Date

Location

Summer 2019

Thursday, 12:15 - 14:00

Start: April 04, 2019

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

04.04.2019

MB-263 CIP-Pool

Pre- and Post-processing with GiD

Tutorial 01
FEM routine
GiD data
Geometry - Plate

2

11.04.2019

MB-263 CIP-Pool

Determination of global mass matrix

Tutorial 02
plot routine
GiD_data_ex2
3

18.04.2019

MB-263 CIP-Pool

Central Difference Method

Tutorial 03

4

25.04.2019

MB-263 CIP-Pool

Newmark Method

Tutorial 04

5

02.05.2019

MB-263 CIP-Pool

Comparison CDM & Newmark Tutorial 05
Geometry - Beam

6

09.05.2019

MB-263 CIP-Pool

Two dimensional truss structures

(based on solution of Tutorial 1)

Tutorial 06
Geometry - Truss
GiD data

7

16.05.2019

MB-263 CIP-Pool

Two dimensional truss structures (continued)

8

23.05.2019

MB-263 CIP-Pool

Nonlinear FEM - the residual format

Tutorial 08

9

MB-263 CIP-Pool

One-Dimensional linear viscoelastic model

Tutorial 09

10

MB-263 CIP-Pool

One-Dimensional perfect elastoplastic model

Tutorial 10
11 MB-263 CIP-Pool

One-Dimensional elastoplastic model with linear isotropic hardening

Tutorial 11
12 MB-263 CIP-Pool

One-Dimensional elastoplastic model with

non-linear hardening law

Tutorial 12

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 in advance and register with your name and matriculation number.

 

Homework
No.
Description Additional
Information
Date of
Submission

1

deadline for registration is

(to be announced)
--.--.----

(to be announced)
--.--.----




Examination

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

Further information regarding the registration will be discussed in the lecture/ tutorial and will be announced on this website.

Exam date: 13.09.2019, 12:00-14:00

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.