## Courses Catalogue

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# Computational Methods in Mechanical Engineering

8452

### Department

Departamento de Engenharia Mecânica e Industrial

6.0

### Teacher in charge

António Paulo Vale Urgueira, Pedro Samuel Gonçalves Coelho

4

84

Português

### Objectives

The purpose of the Computational Methods in Mechanical Engineering course is to provide the student with the ability to solve complex engineering problems with the help of the most recent software available. Besides acquiring theoretically knowledge about the finite element method and also about structural optimization the student acquires skills on the use of software that allows him to solve practical problems, such as MATLAB and ANSYS.

None.

### Subject matter

Introduction to the symbolic manipulation program MATLAB. MATLAB programming language applied to the matrix structural analysis. Solution of systems of linear equations. Introduction to the finite element method. Finite element method in beams. Calculation of deformation, bending moment diagrams and shear diagrams on beams. Problems with eigenvalues and eigenvectors. Static analysis, dynamic (natural frequencies), instability (elastic buckling) and harmonic (vibration). MATLAB applications involving structures composed with elements such as bars and beams. Introduction to finite element commercial software ANSYS. Comparison of results between MATLAB and ANSYS solving beams problems. Introduction to the ANSYS programming language of (APDL - ANSYS Parametric Design Language).

Solution of steady state heat transfer problems with the finite element method. Poisson differential equation. Solution of heat transfer and shaft torsion problems. Solution of plane elasticity problems by the finite element method. Applications in two-dimensional and three-dimensional with ANSYS. Modelling and solving linear and nonlinear problems.

Formulation of structural optimization problems. Optimization of size, shape and topology. Constrained and unconstrained optimization. Lagrange multiplier concept. Linear and nonlinear optimization. Optimality conditions (KKT). Continuous and discrete optimization. Algorithms based on gradients. Evolutionary algorithms. Solution of size structural optimization problems using MATLAB and ANSYS programs.

### Bibliography

An Introduction to the Finite Element Method

J.N. Reddy

McGraw-Hill

Problemas de Elementos Finitos em MATLAB

A.J.M. Ferreira

Fundação Calouste Gulbenkian

Método dos Elementos Finitos - Técnica de Simulação Numérica em Engenharia

Teixeira-Dias, Pinho-da-Cruz, Fontes Valente e Alves de Sousa

ETEP - Edições Técnicas e Profissionais

Introduction to Optimum Design

Jasbir S. Arora

McGraw-Hill

### Teaching method

Lectures and laboratory sessions.

### Evaluation method

The continuous evaluation finishes at the last day of classes in the semester and it consists of two projects and two mini-tests:

1st Project ( TR1 ) – Individual work.

2nd Project ( TR2 ) – Work group (maximum of three people).

1st Test ( T1 ) – Individual and covering first part of the contents of the classes (FEM).

2nd Test ( T2 ) – Individual and covering second part of the contents of the classes (Optimization).

All the projects and the test are mandatory and the attendance to the classes requested. The projects require the elaboration of reports and must have a minimum grade of 10 points. To be approved in the discipline, the student must have positive weighted average for the four classifications, computed by the following formula,

0,3 x TR1 + 0,2 x TR2 + 0,25 x T1 + 0,25 x T2  >= 10

In the case of failure in the previous evaluation it is possible performing an Exam (E) being the approvation dependent on:

0,3 x TR1 + 0,2 x TR2 + 0,5 x E >= 10

The minimum for the Exam is 9,5val. The projects here correpond to the previous mandatory projects developed during the semester.