2024
Computational Mechanics and Optimization
Name: Computational Mechanics and Optimization
Code: EME13149M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mechanical Engineering
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
At the end of the course, students should be able to:
1. Understand and comprehend the principles and foundations of computational methods applied to mechanical engineering.
2. Use computational tools and resources for the analysis and solution of problems in computational mechanics.
3. Implement numerical methods to solve mechanical engineering problems, including linear algebra, root finding, data interpolation, numerical differentiation and integration, ordinary and partial differential equations, and mechanical system optimization.
4. Develop analytical and numerical implementation skills to solve problems considering convergence rate, error, heuristics, and algorithm efficiency.
5. Apply computational methods in the formulation and resolution of problems in applied areas such as structural analysis, thermodynamics, fluid dynamics, and process optimization, demonstrating adaptability and innovation skills.
1. Understand and comprehend the principles and foundations of computational methods applied to mechanical engineering.
2. Use computational tools and resources for the analysis and solution of problems in computational mechanics.
3. Implement numerical methods to solve mechanical engineering problems, including linear algebra, root finding, data interpolation, numerical differentiation and integration, ordinary and partial differential equations, and mechanical system optimization.
4. Develop analytical and numerical implementation skills to solve problems considering convergence rate, error, heuristics, and algorithm efficiency.
5. Apply computational methods in the formulation and resolution of problems in applied areas such as structural analysis, thermodynamics, fluid dynamics, and process optimization, demonstrating adaptability and innovation skills.
Contents
1. Modelling and engineering problem solving. Conservation laws. Importance of numerical methods in engineering. Computational arithmetic.
2. Polynomial interpolation: Polynomial interpolation (Newton and Lagrange). Splines.
3. Numerical differentiation and integration: Finite differences. Newton-Cotes formulas. Gaussian quadrature.
4. Non-linear equations: Bisection, false position, secant, and Newton-Raphson methods.
5. Systems of linear equations. Gaussian elimination method. Triangular factorizations. Gauss-Seidel method.
6. Ordinary differential equations: Initial value and boundary value problems. Their application in engineering. Euler, Runge-Kutta, and finite difference methods.
7. Partial differential equations: Elliptic, parabolic, and hyperbolic equations. Their application in engineering problems. Explicit and implicit methods. Finite difference method.
8. Optimization methods: Direct and gradient methods. Applications in mechanical engineering.
2. Polynomial interpolation: Polynomial interpolation (Newton and Lagrange). Splines.
3. Numerical differentiation and integration: Finite differences. Newton-Cotes formulas. Gaussian quadrature.
4. Non-linear equations: Bisection, false position, secant, and Newton-Raphson methods.
5. Systems of linear equations. Gaussian elimination method. Triangular factorizations. Gauss-Seidel method.
6. Ordinary differential equations: Initial value and boundary value problems. Their application in engineering. Euler, Runge-Kutta, and finite difference methods.
7. Partial differential equations: Elliptic, parabolic, and hyperbolic equations. Their application in engineering problems. Explicit and implicit methods. Finite difference method.
8. Optimization methods: Direct and gradient methods. Applications in mechanical engineering.
Teaching Methods
In theoretical classes, the fundamental principles of different numerical solution methods are presented and discussed. Audio-visual resources and practical examples are utilized to facilitate the understanding of concepts, and interactive discussions are encouraged to promote student participation. During theoretical-practical classes, students are encouraged to apply the knowledge they have acquired in practical exercises that simulate real engineering problems. The study of real cases is used to illustrate the application of computational methods in practical contexts, fostering discussions on the best approaches. Students are guided to use specific tools to implement algorithms and numerical methods to solve the proposed problems. This work promotes both theoretical and practical deepening, allowing students to explore the interdisciplinary connections between numerical methods, optimization, computing, and mechanics.
Assessment
The assessment consists of the following components:
- Practical assignments completed throughout the semester [P1, P2, P3, P4, P5];
- Tests [T1, T2] or a final exam [E].
If the student chooses the continuous assessment option, the final grade (FG) is calculated using the following formula:
FG = 0.6x(P1+P2+P3+P4+P5)/5 + 0.4x(T1+T2)/2
Where Pi, i=1, 2, ?5 represents the grade obtained in each of the practical assignments and Tj, j=1, 2, represents the grade obtained in each of the tests. Each practical assignment and test must have a minimum grade of 7.0.
If the student chooses the final assessment option, the final grade is calculated using the following formula:
FG = 0.4x(P1+P2+P3+P4+P5)/5 + 0.6xE
Where E is the grade obtained in the exam, which must be equal to or greater than 7.0.
- Practical assignments completed throughout the semester [P1, P2, P3, P4, P5];
- Tests [T1, T2] or a final exam [E].
If the student chooses the continuous assessment option, the final grade (FG) is calculated using the following formula:
FG = 0.6x(P1+P2+P3+P4+P5)/5 + 0.4x(T1+T2)/2
Where Pi, i=1, 2, ?5 represents the grade obtained in each of the practical assignments and Tj, j=1, 2, represents the grade obtained in each of the tests. Each practical assignment and test must have a minimum grade of 7.0.
If the student chooses the final assessment option, the final grade is calculated using the following formula:
FG = 0.4x(P1+P2+P3+P4+P5)/5 + 0.6xE
Where E is the grade obtained in the exam, which must be equal to or greater than 7.0.
Teaching Staff
- António Rui de Oliveira Santos Silva Melro [responsible]
Certificações
