Course MV-TM-86012-K-4
Finite Elements (3V+1U, 6.0 LP)
Course Type
SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
---|---|---|---|---|---|
- | K | Lecture with exercise classes (V/U) | 6.0 CP | 124 h | |
3 | V | Lecture | 42 h | ||
1 | U | Lecture hall exercise class | 14 h | ||
(3V+1U) | 6.0 CP | 56 h | 124 h |
Basedata
Contents
- Principles of the numerical solution for boundary value problems (weighted residuals, collocation and Ritz methods for trusses and beams)
- One-dimensional discretization with the Finite Element Method (FEM)
- Element technology for one- and two-dimensional problems (shape functions, numerical integration, isoparametric concept).
- Assembly of the global equation system (element stiffness matrix, element residuals)
- Truss and beam elements
- Displacement and mixed-formulation based elements for plane elasticity problems
Competencies / intended learning achievements
1. Lecture
The students are able to
- Describe and apply several numerical methods for boundary value problems from the field of engineering mechanics
- Formulate truss and beam elements
- Calculate shape functions and their derivatives in the scope of the isoparametric concept
- Construct and apply shape functions for finite elements in two dimensional models
- Calculate plane elasticity problems
2. Exercises
The students are able to
- Apply various numerical methods on truss and beam constructions with Matlab
- Implement truss and beam elements in DAEdalon
- Calculate truss, beam and plane elasticity problems with DAEdalon
- Develop, implement and test element formulations
Literature
- Gross, Hauger, Wriggers: Technische Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
- Gross, Hauger, Schröder, Werner: Formeln und Aufgaben zur Technischen Mechanik 4 – Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, Springer
- Wriggers: Nichtlineare Finite-Element-Methoden, Springer
- Silber, Steinwender: Bauteilberechnung und Optimierung mit der FEM
- Bathe: Finite Element Methoden, Springer
- Hughes: The Finite Element Method, Prentice Hall
- Zienkiewicz, Taylor: The Finite Element Method: The Basis, Butterworth-Heinemann
- Zienkiewicz, Taylor: The Finite Element Method: Solid Mechanics, ButterworthHeinemann
Materials
Lecture presentation sheets, Lecture notes, Exercises, DAEdalon, Matlab. For further information and course materials please consider the corresponding OLAT-course.
Requirements for attendance (informal)
Knowledge of Continuum mechanics is an advantage
Modules:
- [MV-TM-279-M-4] Engineering Mechanics IV (M, 4.0 LP)
- [MV-TM-7-M-1] Applied Mechanics I (M, 5.0 LP)
- [MV-TM-8-M-4] Applied Mechanics II (M, 5.0 LP)
- [MV-TM-9-M-4] Engineering Mechanics III (M, 5.0 LP)
Requirements for attendance (formal)
None
References to Course [MV-TM-86012-K-4]
Module | Name | Context | |
---|---|---|---|
[MV-TM-136-M-4] | Finite Elements | P: Obligatory | 3V+1U, 6.0 LP |
[PHY-SP-4-M-7] | Schwerpunktmodul Technische Mechanik | WP: Obligation to choose | 3V+1U, 6.0 LP |
Notes on the module handbook of the department Mechanical and Process Engineering
Ausnahmen: