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Advanced Structural Analysis

Code 15259
Year 2
Semester S1
ECTS Credits 6
Workload TP(60H)
Scientific area Aeronautics and Astronautics
Entry requirements -
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. Introduction to the Finite Element Method: introduction to variational calculus (functionals); approximate methods (Rayleigh-Ritz and Galerkin).
2. Formulation of 1D Problems: discrete elastic systems; variational formulation; one-dimensional finite elements (truss, beam, and plane frame); assembly of the stiffness matrix; boundary conditions; coordinate transformation.
3. Formulation of 2D and 3D Problems: plane stress state; two-dimensional finite elements (triangular and rectangular); three-dimensional finite elements (tetrahedral and hexahedral).
4. Isoparametric Finite Elements: quadrilateral element; function integration (Gauss-Legendre quadrature).
5. Dynamic Analysis: numerical integration of differential equations; equations of motion of structures; time integration; application to aerospace structures.
6. Modal Analysis: natural frequencies and vibration modes; application to aerospace structures.
7. Aeroelasticity: static and dynamic aeroelasticity.
Main Bibliography 1. Gamboa. P.V., Apontamentos da unidade curricular – Cálculo Estrutural Avançado, ~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.
The assessment of this subject is based on two written tests (T1 and T2) and a set of asignments (T3).
The learning process mark is given by T=0.25T1+0.25T2+0.5T3. 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+0.5T3. The final mark is F=larger(T,E). Approval occurs for F = 10.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2025-09-11

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