Finite Elements Method

Code:

EM0065

Acronym:

MEF

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2017/2018 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEM	53	Syllabus since 2006/2007	5	-	6	45,5	162

Teaching language

Portuguese

Objectives

This course aims to give students an insight into finite element methods applied to the analysis of solids and structures.

Learning outcomes and competences

At the end of the course, students should be capable of programming finite element methods to linear and non linear problems. They should also be capable of discussing about the development of new elements and should be able to interpret results of the most varied problems.

Working method

Presencial

Program

1. Problem formulation on Solid Mechanics 2. Energy Methods: an overview on energy methods on Structural Mechanics- theorems of displacement 3. Finite Elements Formulation; General Method: definition, stages, Finite Elements formulation – displacement 4. 2d elements; Interpolation- shape functions, shape functions demands; function deduction from polynomials; Lagrange polynomials; “Serendipity” polynomials; shape functions in natural coordinates 5. 3d elements, beam and plate elements 6. Vibrations and Dynamic  Analysis by the Finite Element Method  7. Materially non linear problems; plasticity 8. Algorithms of non linear solution 9.  Non linear elasticity, geometrically non linear

Mandatory literature

Oñate Eugenio; Sructural Analysis with the Finite Element Method- Vol1 e Vol2, Springer, 2009
Reddy, J. N.; An Introduction to the Finite Element Method. ISBN: 0-07-112799-2
Zienkiewicz, O. C.; The finite element method. ISBN: 0-07-084174-8(vol.1)
Zienkiewicz, O. C.; Finite elements and approximation
COOK, R. D; MALKUS, D. S. and PLESHA, M. E; Concepts and Applications of Finite Element Analysis, John Wiley & Sons, 1989.
Zienkiewicz, O. C.; The finite element method. ISBN: 0-07-084072-5
Cook, Robert D.; Finite element modeling for stress analysis. ISBN: 0-471-11598-3
Cook, Robert D.; Concepts and Applications of Finite Element Analysis. ISBN: 0-471-03050-3
Smith, I. M.; Programming the finite element method. ISBN: 0-470-84970-3

Complementary Bibliography

Hinton, E.; Finite element programming. ISBN: 0-12-349350-1
Owen, D. R. J; Finite elements in plasticity. ISBN: 0-906674-05-2
Hughes, Thomas J. R.; The finite element method. ISBN: 0-13-317017-9
F. Teixeira-Dias,... [et al.]; Método dos elementos finitos. ISBN: 978-972-8480-25-7
BATHE, K. J. ; Finite Element Procedures, Prentice-Hall, 1996
Szabó, Barna; Finite element analysis. ISBN: 0-0471-50273-1
CRISFIELD, M .A.; Finite Element Procedures for Structural Analysis, Pineridge Press, Vol. 1, 1986

Teaching methods and learning activities

Theoretical classes and theoretical-practical classes Theoretical classes- presentation of course’s themes Theoretical-practical classes- individual assignments orientation

Software

Abaqus 6.2
Ansys 5.7
Matlab 6 R12.1
Fortran 5.0

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Participação presencial	0,00
Trabalho laboratorial	50,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	71,00
Frequência das aulas	49,00
Trabalho laboratorial	42,00
Total:	162,00

Calculation formula of final grade

Final Mark is based on average grade of the assignments and « exams. Minimum of 7 values in each component of the evaluation.

Examinations or Special Assignments

An assignment on Finite Element programming

Special assessment (TE, DA, ...)

A written exam.
The computer assignment has to be done during the first semester.

Classification improvement

Students can improve their grade by attending Recurso exam.