# Finite Element Method

10455

### Department

Departamento de Engenharia Civil

6.0

### Teacher in charge

Corneliu Cismasiu

5

Português

### Objectives

The finite element method is one of the most important tools used
in structural analysis. The method was introduced in the early
sixties, since then its use has been spread to several scientific
domains, namely in several fields of solid and fluid mechanics.

In this course the finite element method will be discussed and
applied to several civil engineering problems. This will allow the
students to understand its potential and usefulness. It will alert
for its limitations.

### Subject matter

1. Presentation
1. Objectives and Program
2. Course structure
3. Evaluation methods
4. Access and use of the available information
2. Introduction
1. Computational Mechanics
2. Discretization Methods
3. Finite Element Method
4. Physical problems/Mathematical models
3. Introduction to FEM
1. Mathematical discrete models
2. Mathematical continuum models
3. Finite Difference Method
4. Finite Element Method
1. Governing system
2. Displacement method
3. Types of finite elements
4. Use of finite elements programs
5. Errors in the analysis
6. Convergence of the solution
5. Appendix
1. Vectors
2. Matrices
3. Tensors

### Bibliography

• K. J. Bathe. Finite element procedures. Prentice-Hall, 1996. (COTA: TA347.BAT)
• O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The finite element method. Volume 1: Its Basis and Fundamentals. Butterworth-Heinemann, 2005. (COTA: TA640.2.ZIE)
• J. N. Reddy. An Introduction to the Finite Element Method. McGraw Hill, 1993. (COTA: TA347.RED)
• A. F. M. Azevedo. Método dos elementos finitos. FEUP, 2003. (http://civil.fe.up.pt/pub/apoio/ano5/mnae/Livro_MEF_AA.htm)
• ### Teaching method

The several subjects will be presented and discussed in both types
of lectures. The several concepts, principles and methods will be
presented at the theoretical classes. The students will then apply
the concepts to simple problems.

At the laboratory classes, the students will finish the problems
started at the lectures. Several applications will then be solved
using the computational tools at hand.

Outside the classes the students are encouraged to study the given
bibliography in order to mature and consolidate the acquired
knowledge.

### Evaluation method

Continuous evaluation without examination or final work.

During the learning period there will be team works which will be classified. The final mark will be calculated using these classifications after an oral examination.

Still it is demanded that the number of unjustified lackes to the lessons does nor exceed one third of the total.