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t.BA.MT.FEM.19HS (Finite Elemente Methode) 
Module: Finite Elemente Methode
This information was generated on: 21 November 2024
No.
t.BA.MT.FEM.19HS
Title
Finite Elemente Methode
Organised by
T IMES
Credits
4

Description

Version: 2.0 start 01 February 2022
 

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 the FE code Abaqus.

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
Knows the mathematical foundations of the FE method and can derive the weak form from the strong form of one- and two-dimensional problems 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 the FE code Abaqus without help F, M K4

Module contents

 1.         Introduction to the FE code Abaqus
1.1       Overview, development, economic benefits of the FE method
1.2       Practical examples
1.3       Practical exercises with the FE code Abaqus
1.3.1    Different modeling techniques of a tension bar
1.3.2    Calculation of an impeller
1.3.3    Calculation of a piston with connecting rod
1.3.4    Calculation of a steam turbine blade
2.         One-dimensional FE problems
2.1       Principle of the FEM using the example of a framework
2.1.1    Stiffness matrix of the tensile/compression bar in the local system
2.1.2    Transformation of the local stiffness matrix to 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 stresses and deformations
2.2       The stiffness matrix of the bending beam
2.2.1    The Euler-Bernoulli beam with distributed load
2.2.2    Superposition of the truss element and the beam element
3.         Mathematical foundations of the FE method
3.1       Basic equations of the linear theory of elasticity
3.2       Strong and weak form using the example of the tensile bar problem
3.3       Differentiability requirements for displacement functions
3.4       Galerkin's method
3.5       Ansatz and shape functions
3.6       Numerical integration according to Gauss
3.7       Construction of element stiffness matrices based on the weak form
4.         Two-dimensional FE problems
4.1       Membrane problems
4.1.1    Strong and weak form of the membrane problem
4.1.2    Stiffness matrix of the 3-node membrane element
4.1.3    Stiffness matrix of the rotationally symmetrical membrane element
4.2       Plane problems
4.2.1    Strong and weak form of the plane problem
4.2.2    The isoparametric concept
4.2.3    The 4-node isoparametric element
4.2.3.1 Stiffness matrix of the 4-node element for the plane stress state 4.2.3.2 Stiffness matrix of the 4-node element for the plane strain state 4.3       Numerical effects
4.3.1    Hourglassing
4.3.2    Shear locking
4.4       Element selection criteria

Teaching materials

 Skriptum "Die Methode der Finiten Elemente – Eine Einführung", slides, own notes

Supplementary literature

 J. Fish, T. Belytschko: A First Course in Finite Elements. John Wiley & Sons, 2007.
M. Hahn, M. Reck: Kompaktkurs Finite Elemente für Einsteiger. Springer Vieweg, 2018.

Prerequisites

  

Teaching language

 (X) German ( ) English

Part of International Profile

 ( ) 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 written 45 min mark 20%
End-of-semester exam exam written 90 min mark 80%

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.

Note

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 21 November 2024.
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 21 November 2024.