Plates and Shells

Code	15253
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Aeronautics and Astronautics
Entry requirements	-
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 developed by the students and commercial packages to perform studies on isotropic or laminated plates and/or shells. It is expected that with the knowledge gained the students become capable of: - interpreting the literature published on this subject including codes; - deriving the fundamental equations for research problems involving plates and shells; - obtaining analytical solutions for plates and shells; - knowing the limitations of the knowledge in plates and shells; - obtaining finite element method solutions for plates and shells using commercial packages and knowing the limitations of the elements so that the more appropriate ones are selected.
Syllabus	1. Introduction. 2. Plates: Classical bending theory of plates: solution methods including series expansion methods, Ritz method and numerical methods. Reissner-Mindlin theory: solution methods using Fourier series and generalized Fourier series based methods, approximate analytical methods and numerical methods. Combined membrane a bending loads. Plate instability. Finite element method applied to plates. 3. Shells: Deformations and stresses in shells. Membrane theory for shells of revolution. Bending theory for cylindrical shells. Bending theory for shells of revolution. Applications. Finite Element Method applied to shells. 4. Computer codes to solve plate and shell problems: Writing Fortran computer codes to solve plate and shell problems. Introduction to Fortran. Plate problems – Navier method, finite differences method and finite element method. Shell problems.
Main Bibliography	1. Gamboa. P.V., Apontamentos da unidade curricular – Placas e Cascas, ~320 acetatos, UBI, 2020. 2. A. C. Ugural, “Stresses in Beams, Plates and Shells”, 3rd edition, CRC Press, Taylor & Francis Group, 2009. ISBN: 978-1-4398-0270-0 3. J. N. Reddy, “Theory and analysis of elastic plates and shells”, 2nd edition, CRC Press, Taylor & Francis Group, 2007. ISBN: 978-0-8493-8415-8 4. J. N. Reddy, “Mechanics of laminated composite plates and shells”, CRC Press, 2004. ISBN: 0-8493-1592-1 5. J. R. Vinson, “The Behavior of Thin Walled Structures: Beams, Plates, and Shells”, Kluwer Academic Publishers, 1989. 6. V. S. Kelkar & R. T. Sewell, “Fundamentals of the Analysis of Shell Structures”, Prentice-Hall, Inc., 1987. 8. R. Szilard, “Theory and Analysis of Plates. Classical and Numerical Methods”, Prentice-Hall, Inc., 1974. 9. E. H. Baker, L. Kovalesky & F. L. Rish, “Structural Analysis of Shells”, Mcgraw-Hill Book Company, 1972.
Teaching Methodologies and Assessment Criteria	This curricular unit is structured in two parts: one essentially theoretical and the other essentially practical. In the first part, the material is transmitted orally with multimedia slideshow support, with additional information written on the board and with example problems solved on the blackboard. In the second part, some programming techniques are taught and computer codes are developed to solve more complex problems. The assessment of this subject is based on one written test (T1) and a set of assignments (T2). The learning process mark is given by T = 0.5T1 + 0.5T2. The mark of the exam is based on a written test (E1) and on the assignments performed during the semester (these assignments are done only once). The exam mark is E = 0.5E1 + 0.5T2. The final mark is F = larger(T,E). Approval occurs for F = 10.
Language	Portuguese. Tutorial support is available in English.