Plates and Shells

Code	10377
Year	3
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Aeronautics and Astronautics
Entry requirements	It is desirable to have taken the following curricular units: Mechanics of Solids and Aerospace Structures I.
Mode of delivery	Face-to-face.
Work placements	There are no work placements.
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 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.
Syllabus	1. Introduction. 2. Plates: Classical bending theory of plates. Solution methods: series expansion methods, Ritz method and numerical methods. Reissner-Mindlin theory. Solution methods: Fourier series and Generalized Fourier series based methods, approximate analytical methods and numerical methods. 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.
Main Bibliography	1. A. C. Ugural, “Stresses in Beams, Plates and Shells”, 3rd edition, CRC Press, Taylor & Francis Group, 2009. ISBN: 978-1-4398-0270-0 2. 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 3. J. N. Reddy, “Mechanics of laminated composite plates and shells”, CRC Press, 2004. ISBN: 0-8493-1592-1 4. J. R. Vinson, “The Behavior of Thin Walled Structures: Beams, Plates, and Shells”, Kluwer Academic Publishers, 1989. 5. V. S. Kelkar & R. T. Sewell, “Fundamentals of the Analysis of Shell Structures”, Prentice-Hall, Inc., 1987. 6. C. A. Mota Soares, “Teoria e Análises de Placas: Métodos Analíticos e Aproximados”, Relatório CEMUL M1.82.01, Jan. 1982. 7. C. M. Mota Soares, “Reservatórios sob Pressão. Análise de Tensões – Deformações”, Relatório CEMUL M4- CMMS, Jan. 1982. 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. 10. S. Timoshenko, S. Woinowsky-Krieger, “Theory of plates and shells”, 2nd Edition, New York: McGraw-Hill, 1959.
Language	Portuguese. Tutorial support is available in English.