Computational Methods In Engineering

Programming knowledge in Matlab.

In the classes of this curricular unit, the following teaching methodologies are employed:

Practical Classes:

Main methodology used:

• Project-based learning, with regular checkpoints including feedforward for assessment, where peer feedback is also emphasized.

Complementary methodologies:

• Content presentation interspersed with in-class debate/discussion;
• Use of digital interaction platforms (Mentimeter, Padlet, among others);
• Analysis and resolution of case studies, in class.

Theoretical-Practical Classes:

• Content presentation interspersed with in-class debate/discussion;
• Analysis and resolution of case studies in class;
• In-class demonstrations, with comparison and discussion of results obtained computationally and analytically;
• Problem-based learning, with application-specific problems in Mechanical Engineering;

 Additionally, an e-learning platform (distance learning) is used to complement and extend the face-to-face classes, highlighting thematic forums as an additional activity for the presentation, discussion, and resolution of doubts and application problems.

A. Apply foundational knowledge in mathematics and programming to subjects taught in other courses of the Bachelor’s and Master’s degrees in Mechanical Engineering;

B. Develop algorithmic and computational approaches in specific applications of Mechanical Engineering;

C. Apply computational mathematical methods in the analysis and resolution of engineering problems;

D. Create programs in script files and Live Script, using advanced Matlab functions and commands, for solving specific applications in Mechanical Engineering;

E. Use Matlab’s AppDesigner for modeling and solving specific applications in Mechanical Engineering;

F. Use numerical modeling methods in the structural calculation of any mechanical component, using proprietary or commercial software.

THEORETICAL-PRACTICAL CLASSES

1. Laplace transform

Definition and properties. Laplace Transform Table. Heaviside function or unit step and Dirac Delta function or unit impulse. Decomposition of a rational fraction into a sum of simple elements (expansion into partial fractions). Inverse Laplace Transform. Convolution Theorem. Troubleshooting initial values ​​and systems of differential equations. Practical application problems – Dynamic Systems. Computational treatment using Matlab and CAS programs.

2. Polynomial interpolation

Polynomial: definition, operations and properties. Taylor Formula and Polynomial. Interpolator polynomial: definition, graphical interpretation and Newton’s formula of divided differences.

3. Differentiation and numerical integration

Formulas for progressive, regressive and centered differences. Trapezoids rule and Simpson rule. Quad Matlab function.

4. Ordinary Differential Equations and Differential Equation Systems. Initial values ​​problem (PVI)

Euler and Runge-Kutta methods (RK2 and RK4). Matlab functions: ODE23, ODE45 and others. Introduction to GUI’s (Graphical User Interface) in Matlab and its application for interface and output of a PVI solution.

5. Partial Derivative Equations (EDPs)

Definition and properties. Laplace, Poisson, Diffusion / Heat, Convex / Transport and Wave equations. Differential problems with initial and boundary conditions. Numerical methods of solving equations with partial derivatives. Introduction to the Finite Difference Method (MDF) and the Finite Element Method (MEF). Weak Formulation (FF) of a differential problem and application of the Ritz-Galerkin (R-G) method. Application problems, mathematical modeling by MDF and MEF, algorithms and respective programming in Matlab.

PRACTICAL CLASSES

1. Programming in Matlab

Matlab programming reviews (one-dimensional and multidimensional arrays, predefined functions, expressions, instructions, creating functions, importing and exporting data, 2D graphics).

Cell Arrays.

Structures.

3D graphics.

Error handling.

Image processing.

App Designer.

Live Script.

2.  Computacional Tools

Conducting workshops/seminars on computational tools relevant to the practice of Mechanical Engineering, specifically for applications for students in the specialties of “Construction and Maintenance of Mechanical Equipment” and “Design, Installation and Maintenance of Thermal Systems”.

3. Final work

Final work with specific applications for students in the specialties of “Construction and Maintenance of Mechanical Equipment” and “Design, Installation and Maintenance of Thermal Systems”.

NAO