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# Hauptinhalt

## Finite Element Methods I (18/1)

### Announcements

Programming homework/Oral examination: a registration for the programming homework/oral examination via mail to your tutorial supervisor is required by 01.02.2019, 11:59pm, the latest. Further details are given below.
23.01.19 - As requested, the due dates for the programming homework/oral examination have been changed

### 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:

• Strong and weak form of balance equations (balance of linear momentum, heat conduction problem, ...)
• Polynomial interpolation and shape functions
• Discretisation of the weak form
• Connectivity/Assembly
• Master element concept
• Numerical integration
• Matrix representation

In the exercises, the focus is placed on:

• Introduction to commercial FE-program
• Applications of the lecture's content
• Programming in MATLAB

### Lectures

Semester

Lecturer

Date

Location

WS 2018/19

Dr.-Ing. Thorsten Bartel

Wednesday, 12:15-13:45

Chemie - HS 1

### Tutorials WS 2018/19

Semester

Date

Location

WS 2018/19

Friday, 12:15-13:45

Maschinenbau - R263
CIP-Pool

Please use the provided documents to prepare yourself for each tutorial.

Tutorial No.

Date

Location

Description

Files

---

---

General Information & Introduction

General
Information
1 19.10 MBI - R263 (CIP-Pool)

Introduction to MATLAB

exercise_01

2

26.10 MBI - R263 (CIP-Pool)

Introduction to MATLAB (continued)

3

02.11 MBI - R263 (CIP-Pool)

Solution via dicretised weak form

exercise 03

4

09.11 MBI - R263 (CIP-Pool)

Solution via dicretised weak form (continued)

5

16.11 MBI - R263 (CIP-Pool)

Semi-analytical analysis of a 1d truss structure

exercise 04

6

23.11 MBI - R263 (CIP-Pool)

FE-implementation of a 1d truss structure consisting of
two elements in MATLAB

exercise 05

7

30.11 MBI - R263 (CIP-Pool)

FE-implementation of a 1d truss structure consisting of
two elements in MATLAB (continued)

8

07.12 MBI - R263 (CIP-Pool)

FE-implementation of a 1d truss structure consisting of
two elements in MATLAB (continued)

9

14.12

MBI - R263 (CIP-Pool)

FE-implementation of a 1d truss structure consisting of
two elements in MATLAB (continued)

post-
processing

10 21.12

MBI - R263 (CIP-Pool)

FE-implementation of a 1d truss structure consisting of
two elements in MATLAB (continued)

11

11.01

MBI - R263 (CIP-Pool)

FE-implementation of a 2d plate problem consisting of
two elements in MATLAB

exercise 06

12

18.01

MBI - R263 (CIP-Pool)

FE-implementation of a 2d plate problem consisting of
two elements in MATLAB (continued)

13

25.01

MBI - R263 (CIP-Pool)

FE-implementation of a 2d plate problem consisting of
two elements in MATLAB (continued)

14

01.02

MBI - R263
(CIP-Pool)

FE-analysis of a 2d notched plate under tension

### Examinations

MMT and Erasmus students will receive a grade for the FEM-I course based on an assignment (programming homework), and on an oral examination about the assignment and about the complete course material (lectures, tutorials).
Note that each student has to solve the programming homework individually on his/her own - if (parts of the) submissions are similar to each other or even identical, the respective submissions will be graded “5.0, not passed”.
A registration (name, matriculation number) for the programming homework/oral examination via mail to your tutorial supervisor is required.

Further information on the assignment will be provided on the examination sheet itself.

 Deadline for registration: 01.02.2019, 11:59pm 28.02.2019, 11:59pm Handout of programming homework: 04.02.2019 14.03.2019 Deadline for submission: 22.03.2019 03.05.2019, 11:59pm Oral examination: 29.03.2019 10.05.2019

Maschinenbau-Studenten: Der Kurs FEM1 ist Teil des Moduls FEM1+FEM2. Die reguläre Modulprüfung in Form einer schriftlichen Klausur findet am Ende der FEM2-Veranstaltung statt.
Diese Modulprüfung umfasst dann die Inhalte von FEM1+FEM2. Eine Einzelprüfung für FEM1 ist deshalb nicht vorgesehen.

### Literature

German literature:
D. Gross, W. Hauger, W. Schnell & P. Wriggers. Technische Mechanik IV. Springer, 2004. (available free of charge from the TU Dortmund internal network)

English literature:
J. Fish, T. Belytschko. A First Course in Finite Elements. Wiley, 2007. (available free of charge from the TU Dortmund internal network)
N. S. Ottosen, H. Petersson. Introduction to the finite element method. Prentice Hall, 1992.
T. J. R. Hughes. The Finite Element Method - Linear Static and Dynamic Finite Element Analysis. Prentice Hall, 2000.
O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The Finite Element Method: Its Basis and Fundamentals, 7th Edition. Butterworth Heinemann, 2013.

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