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Methode der Finiten Elemente I (18/1)

Finite Element Methods I (18/1)

Announcements

The grades of the FEMI - Assignments can now be found on the notice board (right next to the elevator) at our institute.

A review for the assignments will take place on Friday, 19.10.2018 at 14.00 in room 165, MB1.

First lecture: 10.10.2018

First tutorial: 19.10.2018


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

     Start: 10.10.2018

Chemie - HS 1

Accompanying documents for the lecture
 

Description

Lecture notes: 1 Prerequisites

On the determinant of the jacobian




Tutorials WS 2018/19
 

Semester

Date

Location

WS 2018/19

Friday, 12:15-13:45

Maschinenbau - R263
CIP-Pool

 

Accompanying documents for the tutorials (download links will be activated during the semester)

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

---

MBI - R263 (CIP-Pool)

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

exercise 06

12

---

MBI - R263 (CIP-Pool)

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

13

---

MBI - R263 (CIP-Pool)

FE-analysis of a 2d notched plate under tension

exercise 07
subroutines

Additional tutorials for download

FE-analysis of a 1d clamped truss using ABAQUS
FE-analysis of a 2d notched plate using ABAQUS




Examinations

MMT and Erasmus students will receive a grade for the FEM1 course which is based on an assignment (programming homework). The programming homeworks are handed out in the last tutorial. If you want to participate in the programming homework in order to obtain a grade for FEM1, please contact your tutorial supervisor in advance and register with your name and matriculation number. 

Deadline for registration:  t.b.a

Deadline for  submission: t.b.a

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.