Numerical Methods in Engineering

Content

Part I: Computational Methods and Algorithms

Variational principles and weighted residual method
Discretization methods (Finite Difference Method, Finite Volume Method, Boundary Element Method, Finite Element Method)
Solving of ordinary differential equations
Overview over the different methods: typical fields of application, performance, limits
Numerical integration
Symbolic mathematics (i.e. Maple)

Part II: Finite Element Method

Finite element formulation for elastodynamic and heat transfer problems
Selected finite elements: beams, solid isoparametric elements, plates, shells
Modeling (e.g. mesh generation, boundary conditions, model checking, postprocessing)
Selected topics: e.g. submodeling, h- and p-refinement, grid free methods, reduced integration
Practical exercises in the fields of stress analysis and heat transfer

Lecturers

Prof. Dr.-Ing. Dallner, Ingolstadt University of Applied Sciences

Prof. Dr.-Ing, Maurer, Landshut University of Applied Sciences

ECTS

8 credits

Taught as

Class, practical exercise, lab exercise

Contact hours

70 hours

Examination

Written exam

Teaching aims

The participants acquire an advanced knowledge of the most important numerical methods and algorithms in engineering applications and have the referring mathematical and technical understanding. They understand linear as well as nonlinear methods and hence are able to apply these numerical methods to engineering problems. They are able to check, evaluate and discuss numerical results.

In particular the participants get familiar with the Finite Element Method (FEM). Based on the thorough understanding of the theoretical background they are able to apply FEM to engineering problems, especially linear structural mechanics, and have exercised this with practical examples using commercial software. The students are able to perform a Finite Element Analysis on their own, including correct modeling of the real physical problem, selection of appropriate Finite Elements, checking and discussion of results. They are able to realize the potential and the limits of FEM.