Finite elements

General data about the module 

Qualification goals

1. After successfully passing the Finite Elements module, students will be able to reproduce the basic concepts and theoretical background of linear FEM. They are able to distinguish the finite element method from other numerical methods, understand the FEM procedure and can apply it to calculate linear elastic boundary value problems in structural mechanics.
2. The students acquire the competence to independently perform a linear FE calculation (to build up and solve a linear numerical model within the framework of FE software) and to independently interpret and evaluate the calculation results.
3. After completion of the module, the students are also able to use a commercial FE program in a basic way.

Content

• Students will receive a basic introduction to FEM. This includes:
  • Mathematical basics
  • Introduction to the calculus of variations
  • Principle of virtual work
  • Element types (type, degrees of freedom, special features, selection) and application areas for the elements
  • Model verification (sources of error, standard tests, convergence)
• Students gain in-depth knowledge of the application of the FEM to discrete problems in linear structural mechanics:
  • Derivation of simple element formulations for trusses / members as well as for structures / beams.
• Students gain in-depth knowledge on the application of FEM in linear continuum mechanics (1D, 2D as well as 3D):
  • Weak form of momentum balance
  • FE discretization (choice of approach function, isoparametric finite elements)
  • Material model
  • Aspects of numerical integration
  • Implementation and programming
• The students gain knowledge about the application of FEM in structural dynamics, especially in the calculation of natural frequencies and eigenmodes.
• For the application of FEM in thermomechanics (heat conduction problems) the students receive a basic overview.
• In the practical exercises, the students learn how to use an FE program (e.g. ANSYS, ABAQUS) and its application to problems in linear structural mechanics.