# Finite Elements for Electrical Engineering

**Year**

0

**Academic year**

2022-2023

**Code**

02035252

**Subject Area**

Energy

**Language of Instruction**

Portuguese

**Other Languages of Instruction**

English

**Mode of Delivery**

Face-to-face

**ECTS Credits**

6.0

**Type**

Elective

**Level**

2nd Cycle Studies - Mestrado

## Recommended Prerequisites

Electromagnetism, Mathematical Analysis, Linear Algebra, Computational Methods for Electrical Engineering

## Teaching Methods

The course is based on two types of classes: 1) theoretical-practical classes, where numerical concepts that describe the finite element method will be presented and discussed, including problem solving; 2) laboratory classes, where a finite element software will be used for developing numerical simulation works with the students. The students will have to present a project on finite element modeling and finite element analysis using the computer program introduced in the classes.

## Learning Outcomes

This course introduces the Finite Element Method (FEM) which is intended for the analysis of coupled and non-coupled thermal and electromagnetic phenomena. After successful attendance of the course, students will:

• have a fundamental knowledge on FEM

• apply the FEM numerical formulation for solving simple ordinary and partial linear differential equations;

• be aware of the considerations required for FEM modelling, and the limitations associated;

• develop a critical analysis for the interpretation of results obtained from the numerical simulation using FEM;

• be able to work with an FEM commercial software for the analysis of elementary coupled and non-coupled thermal and electromagnetic problems.

## Work Placement(s)

No## Syllabus

1. Maxwell’s equations. Electrostatic fields. Magnetostatic fields. Magnetodynamic fields.

2. Calculus of variations. Fundamental Lemma of variational calculus. Variational methods. Ritz Method. The Method of Weighted Residuals.

3. Finite element modelling. Discretization of the domain. Boundary conditions. Numerical solution. Analysis of elementary electrostatic, magnetostatic, magnetodynamic and thermal problems.

4. Finite element error analysis. Convergence of solution. Accuracy of the solution.

5. Introduction to a finite element software. Environment and graphic representation.

6. Pre-processing. Concepts on creating model geometries. Concepts on creating meshes. Physical modelling.

7. Model processing. Numerical solvers.

8. Analysis of the results. Post-processing.

9. Building some numerical models. Magnetic applications. Electric applications. Thermal applications. Coupled applications.

## Assessment Methods

Assessment

*Resolution Problems: 10.0%*

*Exam: 40.0%*

*Project: 50.0%*

## Bibliography

• Salon, S. J. (1995) Finite element analysis of electrical machines, Kluwer Academic Publishers (Cota: C7410-SAL/B).

• Ida, N. (1997) Electromagnetics and calculation of fields, 2nd ed., Springer (Cota: C7400-IDA/B).

• Silvester, P. P. (1996) Finite elements for electrical engineers, 3rd. ed., Cambridge University Press (Cota: C7410-SIL).

• Jin, J. (1993) The finite element method in electromagnetics, John Wiley & Sons (Cota: C7410-JIN).

• Sadiku, N. O. (1992) Numerical techniques in electromagnetics, CRC Press (cota: B5000-MAT/B).

• Reddy, J. N. (2006) An introduction to the finite element method, 3rd ed., McGraw-Hill (cota: B-519.6-RED).