t.BA.MT.FEM.19HS (Finite Elemente Methode)
Module: Finite Elemente Methode
This information was generated on: 26 September 2021
No.
t.BA.MT.FEM.19HS
Title
Finite Elemente Methode
Organised by
T IMES
Credits
4

### Description

Version: 1.0 start 01 February 2020

#### Short description

Participants are introduced to the structural mechanics and mathematical foundations of the finite element method and learn to work on linear strength problems with a commercial FE code.

#### Module coordinator

Pfrommer Ralf (pfro)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels Form the stiffness matrix in the local system of single dimensional elements of rods and beams and transform it to the global system F, M K4 Incorporate the boundary conditions into the overall stiffness matrix F, M K4 Name the various non-linearities of a structural-mechanical problem and indicate their solution methods and examples F, M K4 Specify displacement approaches for two-dimensional elements and criteria that a displacement approach must meet F, M K4 Describe the concept of isoparametric elements and the numerical calculation of their element matrices F, M K4 Explain and recognize various undesirable numerical effects in FE-calculations F, M K4 Carry out, plausibilise and evaluate linear calculations with a commercial FE program without help F, M K4

#### Module contents

1             Introduction
1.1           Overview, historical development, economical value
1.2           Examples from practice
1.3           Modules of commercial FE-software
2             One-dimensional FE-problems
2.1           FE principle at the example of a half-timbered construction
2.1.1        Stiffness matrix of a push/pull rod in the local system
2.1.2        Transformation of the local stiffness matrix into the global system
2.1.3        Compilation of the overall stiffness matrix
2.1.4        Consideration of boundary conditions and loads
2.1.5        Calculation of stress and deformation
2.2          The stiffness matrix of a bending beam
2.2.1        Euler-Bernoulli-Beam with normal force
2.2.2        Timoshenko-Beam
2.3          Outlook to nonlinear problems
2.3.1        Types of nonlinearities
2.3.2        The Newton-Raphson method
2.3.3        Elastic-plastic pushrod with contact
3            Two-dimensional FE-problems
3.1           Displacement law
3.2           Panel elements for plane stress and plane strain
3.2.1        Simple elements
3.2.1.1       Constant strain triangle element
3.2.1.2       Rectangular element
3.2.2        Isoparametric elements
3.2.2.1       Transformation to the unit element
3.2.2.2       Numerical integration
3.2.2.3       Stress in the element
3.3           Rotationally symmetric elements
3.3.1        Rotational symmetric stress state
3.3.2        Quadrilateral element
4            Three-dimensional FE-problems
4.1          Continuum elements
4.1.1        General requirements
4.1.2        Tetrahedrons
4.1.3        Hexahedrons
4.1.4        Hybrid elements
4.2          Special effects
4.2.1        Hour glassing
4.2.2        Shear-Locking
4.2.3           Criteria for element seleciton

#### Teaching materials

Will be announced at the beginning of the semester

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

#### Module structure

Type 3a
For more details please click on this link: T_CL_Modulauspraegungen_SM2025

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester exam report written written 45 min group mark mark 20% 20% End-of-semester exam exam written 90 min mark 60%

#### Remarks

The contents of this module require a good command of the material of Analysis 1 and 2, Algebra and Statistics 1 and 2 as well as statics and mechanics of materials.

#### Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.
Course: Finite Elemente Methode - Praktikum
No.
t.BA.MT.FEM.19HS.P
Title
Finite Elemente Methode - Praktikum

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.
Course: Finite Elemente Methode - Vorlesung
No.
t.BA.MT.FEM.19HS.V
Title
Finite Elemente Methode - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 01 August 2099.