Sprungmarken

Servicenavigation

Hauptnavigation

Sie sind hier:

Hauptinhalt

Nichtlineare Finite-Elemente-Methoden (9)

Nonlinear Finite Element Methods (9)

Announcements

 

The next lecture will be held in room 165 at 08:30 on Monday, 10.12.2018.


Contents

This course discusses the finite element method, discretization techniques and solution strategies for problems in solid mechanics at large deformations.

  • Repetitorium of kinematics, stresses, balance laws and hyperelasticity
  • Strong and weak forms of balance of linear momentum in spatial and material description
  • Spatial discretization of the weak form in spatial and material description 
  • Linearization and stiffness matrix
  • Nonlinear solution strategies
    • Newton's method
    • line search methods
    • arc length methods (passing limit points, e.g. snap-through)
  • Dirichlet variational principle
  • Thermomechanically coupled problems
  • Transient problems


Prerequisites

Successful completion of the introduction course on Finite Element Methods I and II or equivalent experience. Experience in nonlinear continuum mechanics and scientific programming in Matlab (or C, C++, Fortran) necessary.


Lectures

Semester Lecturer Date Location
Winter 2018/19 Prof. Dr.-Ing. Andreas Menzel

Monday, 8:30 - 10:00

Tuesday, 10:15 - 11:45

MB-Building, Room 165

 

Accompanying documents for the lectures
Chapter Content Files
0 Table of contents, Selected references, Notation Chapter 0
1 Continuum thermomechanics, Kinematics, Balance laws, Constitutive relations Chapter 1
2 Piecewise polynomial interpolation, Shape functions, Coordinate mapping Chapter 2
3 Discrete kinematics, Discretisation of deformation map, Implementation Chapter 3
4 Discretisation of element contributions, Time discretisation, Elasticity Chapter 4
5 Discretisation of thermoelasticity, Monolithic solution scheme Chapter 5
6 Non-linear truss element in three dimensions, One-dimensional hyperelasticity Chapter 6
7 Solution methods for quasi-static nonlinear problems Chapter 7
8 Deformation dependent loads Chapter 8


Tutorials

Semester Supervisor Date Location
Winter 2018/19 Dipl.-Ing. Rolf Berthelsen

Monday, 8:30 - 10:00

Tuesday, 10:15 - 11:45

MB-Building, Room 163

 

Accompanying documents for the tutorials

All participants are requested to download the exercises in preparation of the respective tutorial.

Tutorial No. Date Description Files
1 22.10.2018 Mesh generation with gmsh: Part 1 -
2 23.10.2018 Mesh generation with gmsh: Part 2 ex02_gmsh.zip
3 06.11.2018 Mesh generation with gmsh: Part 3 -
4 13.11.2018 Implementation of a non-linear finite element programme:
Part 1 - Finite elasticity
fem2d_quad4.zip
5 20.11.2018 Implementation of a non-linear finite element programme:
Part 2 - Finite elasticity
-
6 26.11.2018 Implementation of a non-linear finite element programme:
Part 3 - Finite thermoelasticity
fem_programme.zip
7 27.11.2018 Implementation of a non-linear finite element programme:
Part 4 - Finite thermoelasticity
-
8 04.12.2018 Implementation of a non-linear finite element programme:
Part 5 - 3d truss elements
-
9 - Implementation of a non-linear finite element programme:
Part 6 - Postprocessing with vtk
-
10 - Implementation of a non-linear finite element programme:
Part 7 - Sparse linear algebra
-


Literature

P. Wriggers: Nonlinear Finite Element Methods, Springer, 2008

J. Bonet, R.D. Wood: Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge, 2008

R. de Borst, M.A. Crisfield, J.J.C. Remmers, C.V. Verhoosel: Non-linear Finite Element Analysis of Solids and Structures, Wiley, 2012

O.C. Zienkiewicz, R.L.Taylor, D.D. Fox: The Finite Element Method for Solid & Structural Mechanics, Butterworth-Heinemann, 2014

G. Dhondt: The Finite Element Method for Three-dimensional Thermomechanical Applications, Wiley, 2004