Computational Modelling of Materials
Code
10414
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Ciências dos Materiais
Credits
3.0
Teacher in charge
Guilherme António Rodrigues Lavareda
Weekly hours
3
Total hours
42
Teaching language
Português
Objectives
The course intends to implement knowledge and develop basic skills, using computational methods, to simulate and analyze simple models of systems behavior or processes evolution.
Prerequisites
To have basic knowledge of Mathematics, Materials Science and Computation (not restrictive)
Subject matter
Part I – Introduction (MatLab / Visual Basic)
- The development environments of MatLab and Visual Basic
- Programming syntaxes
- Generation and manipulation of vectors and arrays
- File reading and writing in different formats
- Programming: Flow control structures and logical tests
- Numeric and symbolic computing
- Simple numerical methods. Error definition in numerical computing. Stopping criterion and tolerance.
Parte II – Scientific computing and materials modelling
- Resolution of linear equation systems
- Experimental data fitting by polynomial functions
- Experimental data fitting - non-polynomial functions
- Experimental data fitting - special methods for functions with more than one variable.
- Inicial variable estimation in numerical methods. Graphical method for the inicial estimation.
- Equation roots – Newton-Raphson method
- Resolution of equation systems for oscillatory movement problems
- Differentiation using finite-difference
- Resolution of ordinary differential equations using the Euler method
- Resolution of ordinary differential equations using the Runge-Kutta method
- Application examples to material modelling and case studies.
Bibliography
• Steven C. Chapra, Applied numerical methods with MATLAB for engineers and scientists, 2ª ed., Mc-Graw Hill, New York, 2008
• Desmond J. Higham & Nicholas J. Higham, Matlab guide, 2ª ed., SIAM, Philadelphia, 2005
• Steven C. Chapra & Raymond P. Canale, Numerical methods for engineers, 2ª ed., Mc-Graw Hill, New York, 1988 (edição mais recente 7ª ed)
• John H. Mathews & Kurtis D. Fink, Numerical methods : using MATLAB, 4ª ed., Pearson, New Jersey, 2004
• Cleve B. Moler, Numerical computing with MATLAB, 1ª ed, The MathWorks, Inc, SIAM, Philadelphia, 2004
• Curtis F. Gerald & Patrick O. Wheathley, Applied numerical analysis, 7ª ed., Addison Wesley. Boston, 2004
Scientific articles of significant relevance .
Teaching method
The course will be given in a classroom equipped with computers (one computer per student).
Initial presentation of the subjects followed by immediate application or simultaneous execution of commands.
Resolution of training questionnaires.
Software used: MatLab