Finite Element Method

Code:

MMC002

Acronym:

MEF

Keywords
Classification	Keyword
OFICIAL	Engineering

Instance: 2024/2025 - 1S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Master in Computational Mechanics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MMC	4	Syllabus since 2011/12	1	-	7,5	70	202,5

Teaching language

English

Objectives

The curricular unit Finite Element Method aims to provide students with knowledge in the area of numerical methods to be applied in structural mechanics and based on Finite Element Method.

It is expected that at the end of the semester, the students have acquired knowledge to use tools in order to build models (discretization, imposition of boundary conditions and material properties) and the correct interpretation of results, getting skills at the elementary level, such as the finite element formulation (establishment of the stiffness matrix, calculating the strain and the stress fields).

Learning outcomes and competences

The students should acquire skills to perform a structural analysis based on the finite element method.

Working method

Presencial

Program

Brief review of the fundamentals of solid mechanics (stress and strain states, constitutive laws).

The Finite Element Method: General. Discrete and continuous problems. Discretization needs. Analysis of two-dimensional linear elastic problems by the Finite Element Method. Equilibrium equation in 2D domain. Decomposition into triangular elements of 3 nodes. Displacement field, stress field; system of nodal forces. Interpolation functions or shape functions. Matrix of deformation [B], matrix of elasticity [D]; stiffness matrix [K]. Load vector. Presentation of the usual shape functions for elements 1D, 2D and 3D triangular and quadrangular hexahedral and tetrahedral. Isoparametric elements. Numerical integration based in the Gauss rule. Formulation of elements to linear elastic analysis. Pre and post processing: major types of mesh generation; establishing of isocurves and its interpretation.

Practical application of the method in mechanical systems.

Mandatory literature

Jacob Fish, Ted Belytschko; A first course in finite elements. ISBN: 978-0-470-03580-1
Cees Oomens, Marcel Brekelmans, Frank Baaijens; Biomechanics. Concepts and Computation, Cambridge University Press, 2009. ISBN: 978-0-521-87558-5

Complementary Bibliography

A. J. M. Ferreira; Problemas de elementos finitos em MATLAB. ISBN: 978-972-31-1329-7

Teaching methods and learning activities

1 theoretical-pratical classe per week with 3h in order to present the contents and their applications.
1 pratical class (2 hours).

Software

ABAQUS
ANSYS Academic Teaching Intro

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	60,00
Trabalho escrito	40,00
Total:	100,00

Eligibility for exams

The students need to do a pratical work.

Calculation formula of final grade

40% work + 60% examination