| Code |
18157
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
MECÂNICA COMPUTACIONAL
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Entry requirements |
N.A.
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Learning outcomes |
To learn and understand the theories and solution methods described, which are necessary to understand engineering problems where plate and shell components are the fundamental elements of a structure. To develop analysis, synthesis and judgment skills by using codes in Fortran/Matlab developed by the students and commercial packages to perform studies on plates and/or anisotropic laminates.
It is expected that with the knowledge gained the students become capable of:
- To interpret the literature published on this subject including codes;
- To derive the fundamental equations for research problems involving plates and shells;
- To obtain analytical solutions for plates and shells;
- To know the limitations of the knowledge in plates and shells;
- To obtain finite element methods solutions for plates and shells using commercial packages and to know the limitations of the elements so that the more appropriate ones are selected.
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Syllabus |
1. Introduction
2. Plates
Classical plate bending theory: Analytical solution methods including Fourier series development (Navier and Lévy Method), Ritz Method, and numerical methods (finite differences and finite element method for plates). Combined membrane and lateral forces. Plate instability. Large deflections.
3. Shells
Stresses and strains in shells. Membrane stresses in shells of revolution. Bending theory of cylindrical shells. Bending stresses in shells of revolution. Applications. Finite element method for shells.
4. Computer Codes for Solving Plate and Shell Problems
Writing codes in Fortran/Matlab to solve plate and shell problems. Introduction to Fortran. Plate problem - Navier and Lévy method, finite difference method, and finite element method. Shell problem.
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Main Bibliography |
[1] Dutra, T.A. (2025). Lectures notes in Plates and Shells, UBI.
[2] Ugural, A. C. (2017). Plates and Shells: Theory and Analysis, Fourth Edition. Taylor & Francis Group. ISBN: 9781315104621
[3] Reddy, J. N. (2017). Energy Principles and Variational Methods in Applied Mechanics. Wiley. ISBN: 978-1-119-08737-3
[4] Reddy, J. N. (2007). Theory and Analysis of Elastic Plates and Shells, Second Edition. Taylor & Francis. ISBN: 978-0-8493-8415-8
[5] Reddy, J. N. (2004). Mechanics of laminated composite plates and shells : theory and analysis. Taylor & Francis. ISBN: 0-8493-1592-1
[6]Timoshenko, S. (2003). Theory of Plates and Shells. Textbook Publishers. ISBN: 9780758184092.
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Teaching Methodologies and Assessment Criteria |
The curricular unit is structured in two parts: a theoretical part and a practical part.
In the first part, the topics are lectured with the support of multimedia slides. Additional information is written on the board and exercises are solved.
In the second part, programming techniques are taught, and computer codes are developed to solve more complex problems.
Evaluation is continuous and carried out in two stages: (i) a written test (TE); and (ii) a set of assignments (TP), evaluating different aspects of the competencies acquired by the students.
The learning process classification is NFA=0.5TE+0.5TP.
Approval occurs when, cumulatively, NFA>=10, TE>=6, and TP>=8.
The condition for exam access is TE>=6 and TP>=8.
The exam evaluation is based on a written test (NE) and the assignments carried out during the semester (the assignments are only done once).
The exam classification is NFE=0.5NE+0.5TP.
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Language |
Portuguese. Tutorial support is available in English.
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