Finite Element Method

Code:

M.EM002

Acronym:

MEF

Keywords
Classification	Keyword
OFICIAL	Computational Methods

Instance: 2021/2022 - 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
M.EM	118	Syllabus	1	-	6	39	162

Teaching language

English

Objectives

1. From the mathematical point of view, knowledge of how to formulate a problem through the Finite Element Method, starting from the strong form of the differential equations, converting them to the weak form, and finally performing the spatial discretization of the problem, is expected.


2. To develop different types of finite elements and assemble the matrices and vectors, which are relevant for the solution of problems in the Mechanics of Solids in terms of displacements. Programming the Finite Element Method for the calculation of solids and structures.


3. Be able to use the Finite Element Method to solve practical problems in Mechanical Engineering through the use of numerical packages (e.g., ABAQUS).

Learning outcomes and competences

Working method

Presencial

Program

• Review of the application of energy methods in structural mechanics and the Finite Element Method: general presentation of energy methods with particular reference to theorems based on displacement formulations.


• Formulation of Finite Elements; General Method: definition, by stages, of the formulation of Finite Elements in terms of displacements.


• Dynamic Analysis by the Finite Element Method: Hamilton Variational Principle, consistently linearized mass matrix, numerical integration of the motion equation (Finite Difference Method and Newmark).


• Material non-linear problems, plasticity: physical motivation, mathematical model and computational aspects for one-dimensional problems. Interaction with the yield surface, Forward-Euler, and Backward-Euler algorithms, consistent tangent matrix.

Mandatory literature

Oñate Eugenio; Sructural Analysis with the Finite Element Method- Vol1 e Vol2, Springer, 2009

Complementary Bibliography

Zienkiewicz, O. C.; The finite element method. ISBN: 0-07-084174-8(vol.1)
F. Teixeira-Dias,... [et al.]; Método dos elementos finitos. ISBN: 978-972-8480-25-7
Jacob Fish; A first course in finite elements. ISBN: 978-0-470-03580-1
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
Reddy, J. N.; An Introduction to the Finite Element Method. ISBN: 0-07-112799-2

Teaching methods and learning activities

Theoretical-Practical classes. In the Classes, the exposition of several theoretical subjects will be made as well as the supervision of individual assignments that will be performed in the period of classes, in the classes and at home.

Software

Abaqus 6.2
Ansys 5.7
Matlab 6 R12.1

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Trabalho laboratorial	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	95,00
Frequência das aulas	39,00
Trabalho laboratorial	28,00
Total:	162,00

Eligibility for exams

Calculation formula of final grade

Final Mark is based on the average grade of the assignment and exam. Minimum of 7 (out of 20) in each component of the evaluation.

Examinations or Special Assignments

An assignment on Finite Element analysis/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 resit exam.

Observations

https://videoconf-colibri.zoom.us/j/89795068917?pwd=dVptMTNFZXFXaDlGUXRXbzRPdUtEdz09



ID da reunião: 897 9506 8917

Senha de acesso: 702671