(Created 2009-08-11.)

THE FINITE ELEMENT METHOD - FIELD PROBLEMS | VSMN05 |

**Aim**

The aim of the course is to give detailed theoretical and practical knowledge on the finite element method to be able to model and analyse general field problems described from a physical context. Common problems within the field of engineering will be studeied, such as, heat flow, flow in pipes, ground water flow and diffusion for both stationary and transient conditions.

*Knowledge and understanding*

For a passing grade the student must

- be able to define linear stationary and transient field problems in 1d-3d and interpret their physical terms.
- from physical relations be able to formulate a mathematical model for the problem.
- be able to transfer a mathematical model, through the weak formulation, to a finite element formulation.
- be able to explain convergence, completeness and compatibility requirements for approximating functions.
- be able to describe the formulation of isoparametric elements and numerical integration.
- be able to define and utilise various types of boundary conditions and loadings.

*Skills and abilities*

For a passing grade the student must

- be able to create finite element models of real problems from a physical described context.
- be able to perform finite element analyses of differing types of engineering problems.

*Judgement and approach*

For a passing grade the student must

- be able to analyse and interpret results from a finite element simulation.
- be able to estimate the reliability of a finite element analysis.

**Contents**

The course consists of lectures, exercise sessions and two compulsory design assignments. In the first part of the course a detailed derivation of all the steps in the finite element formulation are given for a one-dimensional heat flow problem: direct approach, strong and weak formulations, approximating functions and weighted residual methods. More advanced problems are gradually added to this basic knowledge, such as, 2- and 3-dimensional field problems. Field problems that are studied: heat flow, flow in pipes, groundwater flow and diffusion. At the end of the course the theory is extended to the study of transient field-problems. The design assignments illustrate the procedure of transferring a design problem into a model suitable for finite element analysis.

**Literature**

Ottosen, N. & Petersson, H.: Introduction to the Finite Element Method. Prentice Hall, 1992.

Olsson, K.-G and Heyden S.: Introduction to the finite element method, problems. Structural Mechanics, Lund 2001.

CALFEM ver 3.4 - A finite element toolbox, KFS i Lund AB, 2004.