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”.

This course unit employs an exclusively continuous assessment methodology, consisting of the following components:

C1 - Theoretical-Practical Learning Activities:

• Weight: 40% (8 points);
• Mandatory presentation and discussion of activities during classes, at a time to be determined;
• Activities not completed or not presented will be graded 0 (zero).

C2 - Application Project in Mechanical Engineering using AppDesigner (Matlab):

• Weight: 60% (12 points);

1. checkpoint - 0 % (4th week of classes – Formative Assessment)
2. checkpoint - 5 % (8th week of classes )
3. checkpoint - 10 % (12th week of classes )
4. Final presentation and discussion – 45% (exam period – schedule to be defined)

• Mandatory completion;
• Each group will be assigned a different topic;
• Final Submission:
1. Report, according to the Master’s Thesis, Project, and Internship Report Template ,  with a maximum of 40 pages (excluding appendices), in PDF format, on the InforEstudante platform;
2. AppDesigner application, via email, to the course instructors. If the files are large, they should be sent via WeTransfer or equivalent;
3. Submission deadline: last day of the first semester exam support period;
• The presentations in the checkpoints will take place during class, with peer feedback provided through a rubric that will be made available on the InforEstudante platform.
• The presentation and discussion of the project will be conducted before a panel of 2 professors, in a public oral session. The total presentation and discussion time should not exceed 1 hour;
• Attendance at all presentations is mandatory (checkpoints and final discussion); thus, students who do not present the checkpoints ou their final project will receive a final grade of NRC (Does Not Meet Conditions);
• Evaluation criteria will be made available on the InforEstudante platform.

FINAL GRADE (FG): FG = C1 + C2 

GENERAL NOTES:

• For the completion of the various components, students should form groups of two members, although individual work may be exceptionally allowed;
• Although all group members must be familiar with the entire project, each student is responsible for different parts, presenting and defending their part in the final discussion. Therefore, the final grade for the projects is individual;
• If applicable, the use of AI must be explicitly indicated and cited;
• If applicable, student workers must inform the professor of any limitations in completing any assessment components by the 3rd week of classes, so that alternatives can be implemented;
• The submission of a report is only mandatory in component C2;
• Additional information about the various components will be made available on the InforEstudante platform throughout the semester.

NAO