Advanced Methods of Discretization

Code:

MMC008

Acronym:

MAD

Keywords
Classification	Keyword
OFICIAL	Engineering

Instance: 2016/2017 - 2S

Active?	Yes
Responsible unit:	Mathematics 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	8	Syllabus since 2011/12	1	-	7,5	70	202,5

Teaching language

English

Objectives

Apprehension of the fundamental concepts of available advanced discretization techniques (meshless methods). Developing the ability to use the knowledge acquired to solve simple computational mechanics problems using meshless methods.

Learning outcomes and competences

Capability to design simple structures and mechanical components.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

It is necessary to have basic knowledge in: Solid Mechanics, Approximation numerical techniques, Algebra, programming.

Program

1-Brief introduction to Matlab.

2-Introduction to Advanced Discretization Techniques

  - Comparison with the Finite Element Method

  - Available Meshless methods

  - kinds of approximation/interpolation functions

  - influence domain concept

  - numeric integration schemes

3-Brief Presentation on Solid Mechanics

  - Hooke’s Law

  - Equilibrium Equations

  - Galerkin Weak Form

  - Discrete Equation System

4-Finite element method

- Formulation: Discretization, integration mesh, shape functions, matrix formulaiton

- Matlab programming 2D problems using linear triangular elements

- Matlab programming 2D problems using quadrilateral elements

5-Meshless Methods

  - Approximation Functions (Moving Least Square Approximants)

  - Interpolation Functions (Radial Point Interpolators)

  - Matrix Formulation

  - Essential and Natural Boundary imposition

6-Numeric Implementation

7-Basic Meshless Software in Matlab (open-source software created by the lecture)

  - Matlab introduction

  - Presentation of the several routines and subroutines of the meshless method software

  - Solving simple examples

  - Extending the software to other fields of computational mechanics

Mandatory literature

Belinha Jorge Américo Oliveira Pinto Universidade do Porto. Faculdade de Engenharia; Meshless methods in biomechanics. ISBN: 978-3-319-06399-7
Liu Gui-Rong; Meshfree methods. ISBN: 978-1-4200-8209-8

Complementary Bibliography

Onate Eugenio; Structural analysis with the finite element method. ISBN: 978-1-4020-8732-5
Ferreira António Joaquim Mendes; MATLAB codes for finite element analysis. ISBN: 978-1-4020-9199-5

Teaching methods and learning activities

Theoretical-Practical classes with exposition of the relevant theory.

Practical classes to solve typical problems at the end of each unit.

Suggestion of problems to be solved individually in class and at home.

It is delivered to all students a copy of a open-source meshless software created by the lecture.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Defesa pública de dissertação, de relatório de projeto ou estágio, ou de tese	10,00
Exame	40,00
Trabalho escrito	50,00
Total:	100,00

Calculation formula of final grade

50% of final exam + 40% of the final report + 10% of the final presentation.

At the end of the semester all students will be evaluated with a final exam rated from 0 to 20 values. Final grades higher than 17 values are conditioned to an oral exam.