Structural Mechanics

Code	10411
Year	5
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Aeronautics and Astronautics
Entry requirements	It is important that students have previously attended the curricular units of Aerospace Structures I and Aerospace Structures II.
Mode of delivery	Face-to-face.
Work placements	There are no work placements.
Learning outcomes	To know techniques for the numerical solution of differential equations in structures. To know and to be able to apply the finite element method. To learn the theoretical fundamentals, the theoretical and practical descriptions of finite element programs, with applications to structures. To analyze the results from a physical point of view. To understand the dynamic behavior of aerospace vehicle structures when subjected to aeroelastic phenomena, considering the design of some critical components. To be able to interpret relevant analysis theories and to know how to apply them to specific cases. It is expected that with the knowledge acquired the students will be able to: - interpret published literature on the subject including codes; - derive the fundamental equations for research problems; - know the limitations of knowledge; - obtain analytical solutions and develop numerical implementations.
Syllabus	1. Numerical integration of differential equations: Strong and weak formulation. Equivalence between formulations. Introduction to the finite element method. 2. Basic concepts: One-dimensional problem. Galerkin approximation. Stiffness matrix. Loads vector. Multilinear functions. Properties of the stiffness matrix. Linear finite elements. Assembly of the stiffness matrix and the global load vector. Boundary conditions. Solution of the equations. 3. 2D and 3D problems: Galerkin approximation. Properties of the stiffness matrix. Stiffness matrix and force vector of the elements. Problem of linear elasticity. 4. Isoparametric finite flement: Bilinear quadrangular element. Numerical integration. Gauss method. 5. Numerical problems. 6. Applications: Commercial programs. Application to aeronautical structures. 7. Modal analysis: natural frequencies and vibration modes. 8. Fluid-structure interaction: Static Aeroelasticity. Dynamic aeroelasticity.
Main Bibliography	1. Gamboa. P.V., Apontamentos da unidade curricular – Mecânica Estrutural, ~500 acetatos, UBI, 2020. 2. J.N. Reddy, An Introduction to the Finite Element Method, Third Edition, McGraw-Hill, 2006. 3. E. Becker, G. Carey and J. Oden, Finite Elements: An Introduction, Vol. I, Prentice Hall, Englewood-Cliffs, 1981. 4. Cook, Malkus, Plesha, and Witt, Concepts and Applications of Finite Element Analysis, 4th Edition, Wiley, 2002. 5. C.A. Mota Soares, Elementos Finitos em Mecânica dos Sólidos, IST/DEM, 1982. 6. K.K. Gupta, J.L. Meek, Finite Element Multidisciplinary Analysis, Seconf Edition, AIAA Education Series, 2003. 7. M.N. Bismarck-Nasr, Structural Dynamics in Aeronautical Engineering, AIAA Education Series, 1999. 8. J.R Wright, J.E. Cooper, Introduction to Aircraft Aeroelsticity and Loads, 2nd Edition, Aerospace Series, Wiley, 2015.
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. In the second part, some cases are studied using student’s written codes and commercial software for finite element analysis.
Language	Portuguese. Tutorial support is available in English.