Examination arrangement

Course content

The course includes finite element discretisation via weak form formulation of various differential equations for multiphysics problems. The main applications are 2- and 3-dimensional field problems in heat conduction and elasticity problems. Finite element formulations of fluid mechanics problem will also be addressed. The popular Multiphysics finite element program COMSOL will be used.

Learning outcome

This multiphysics-oriented course gives a detailed introduction to the finite element methods used for solving different field problems in engineering science and multiphysics domains, including structural, heat transfer as well as fluid mechanics problems. Formulation, understanding and practice of the finite element methods will be emphasized.

Finite element method for engineering sciences has the following objectives:

Knowledge:

Candidates will learn the knowledge of

- Formulations for 1D, 2D and 3D stress problems

- Formulations for various multiphysics problems problems

- Strong form, weak form and Galerkin method

- Interpolation functions for various elements

- Iso-parametric elements

- Stiffness matrix and load vectors

- Numerical integration methods

- Convergence criterion

- Analysis of finite element analysis results

- Structure of a finite element program

Skills:

Candidates will be able to:

- Use the Galerkin method to derive the finite element equation for a given differential equation

- Derive the stiffness matrix and load vectors of 1D elements in detail

- Derive the load vectors for plane elements

- Establish interpolation functions for simple elements

- Build the global stiffness matrix equations based on single element equation

- Use multiphysics COMSOL program to solve a number of engineering problems

General competence:

Candidates will:

- Know the fundamentals of finite element methods for solving diverse multiphysics problems

- Understand how the finite element calculations were carried out

- are able to critically review the finite element results obtained

Learning methods and activities

Lectures and exercises. 2/3 of the exercises approved is minimum for exam admittance. A computer exercise based on the COMSOL program is mandatory. Lectures, exercises and examination papers will be given in English only. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

• Exercises

Further on evaluation

If there is a resit examination, the examination form may be changed from written to oral.

Specific conditions

Recommended previous knowledge

The course is based on basic courses in statics, strength of materials, and continuum mechanics (Mechanics 3).

Course materials

N. Ottosen & H. Pettersson: Introduction to the Finite Element Method (preliminary);

Jacob Fish and Ted Belytschko: A First Course in Finite Elements;

Zhiliang Zhang: Finite Element Method Lecture notes.

Credit reductions