### Graduate

**AE-245: Finite Elements I (2004, 2005, 2007, 2010, 2011, 2013-2017, 2019)**Basis of the finite element method. Finite elements in heat conduction and elastostatics. Element formulation based on the weak form and principle of total potential energy. Isoparametric elements, mixed formulation. Introduction to calculus of variations. C0 beam and plate elements. Shear locking effect. Bibliography: Hughes TJR, The Finite Element Method, Prentice-Hall, Englewood Cliffs, New Jersey, 1987; Strang G, Fix GJ, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973; Weinstock R, Calculus of Variations with Applications to Physics and Engineering, McGraw-Hill, New York, 1952.

**AE-722: Analysis of Aerospace Structures (2020-2023)**Bending-torsion of thin-walled beams with open and closed cross sections; axial constraint; structural idealization; deflections. Analysis of wing and fuselage structures; effect of cutouts; fuselage frames; ribs. Shear lag. Analysis of connections and fittings. Finite element modeling. Bibliography: Megson THG, Aircraft Structures for Engineering Students, Elsevier, 2007; Bruhn EF, Analysis and Design of Flight Vehicle Structures, TriOffset, Cincinnati, 1973; Flabel JC, Practical Stress Analysis for Design Engineers, Lake City Publishing Company, 1997.

**MT-717: Introduction to Materials and Fabrication Processes (2019-2024)**Metallic materials: mechanical properties; metal alloys for aeronautical applications. General concepts: ceramic materials, polymers and carbon based: applications. Mechanics of materials: basic assumptions. Material behavior: elastic; plastic; inelastic; viscoelastic. Types of mechanical failure: excessive plastic deformation; excessive elastic deformation; fracture; plastic instability. Theory of plastic yielding: yield criteria (von Mises, Tresca, Levi-Mises, Hill). Fundamentals of metal forming: process classification; influence of anisotropy, strain rate, temperature, friction and lubrication. Fabrication of tubes and sheets: extrusion; rolling; drawing. Conventional and non-conventional fabrication processes: sheet forming; volume forming; conventional machining. Introduction and presentation of main aircraft components. Introduction to the fabrication of fuselages: main components and fabrication processes, sealing and riveting. Introduction to wing and empennage assembly. Introduction to composites: materials and fabrication processes. Landing gear manufacture: materials and fabrication processes. Development of new fabrication processes: additive manufacture. Bibliography: Dieter GE, Mechanical Metallurgy – SI Metric Edition, McGraw-Hill Book Co., 1988; Chakrabarty J, Applied Plasticity, Springer, 2nd edition, 2010; Hosford WF, Caddell RM, Metal Forming: Mechanics and Metallurgy, Cambridge University Press, 4th edition, 2011; Verlinden B, Driver J, Samajdar I, Doherty RD, Thermo-Mechanical Processing of Metallic Materials, Elsevier, 2007; ASM Handbook, Volume 14, Forming and Forging, electronic files, 1998.

**MP-206: Analysis and Design of Composite Structures (2015-2022)**Classification, terminology, macromechanic response. Macromechanical behavior of lamina: stress and strain transformation, constitutive relations. Lamina Stiffness and flexibility. Engineering constants. Lamina stress x strain relations; material invariants. Lamina strength, biaxial strength criteria. Lamina micromechanical behavior: representative volume, blending rules and elasticity based approaches. Laminates: bending of thin plates, classical theory of lamination, Mindlin theory for laminates, special laminates, hygrothermal effects. Bending, buckling and vibration of laminated plates. Aeroelasticity of laminated plates. Analysis and design of laminates. Advanced topics in analysis and design of impact on composites. Fracture mechanics applied to composites. Notions of composite structure optimization. Bibliography: Jones RM. Mechanics of Composite Materials, 2nd ed., Taylor & Francis, 1999; Reddy JN Mechanics of Laminated Composite Plates and Shells: theory and analysis, 2nd ed. CRC Press, 2004; Gurdal Z, Haftka RT, Hajela P. Design and Optimization of Laminated Composite Materials, New York, NY: Wiley, 1999.

**MP-703: Design and Manufacture of Composite Structures (2012-2023)**Introduction to composite materials: classification, anisotropy, homogeneity. Fibers for high performance composites. Thermofixed and thermoplastic resins. Cure kinetics and rheology of thermofixed resins. Concepts of design of composite structures. Application of composites in aeronautic construction. Fabrication of thermofixed matrix composite materials: manual layup, automatic layup, filament winding, pultrusion and infusion. Numerical modeling. Fabrication of thermoplastic matrix composite materials. Metallic and composite molds. Cutting and assembly. Inspection, experimental characterization and testing of composites. Mechanical joints and glued joints. Repairs. Bibliography: Daniel IM, Ishai O, Engineering Mechanics of Composite Materials, 2nd edition, Oxford University Press, 2006; Strong B, Fundamentals of Composites Manufacturing: Materials, Methods and Applications, SME Publications, 1989; Morena JJ, Advanced Composite Mold Making, Van Nostrand Reinhold Co., New York, 1988.

**MP-291: Dynamics of Mechanical Systems (2003, 2010, 2011, 2013, 2014)**Mathematical description of mechanical models: kinetics and kinematics of multibody and hybrid systems. Kinematics of a point and system of points, coordinate transformation, relative movement, kinematics of rigid bodies. Introduction to calculus of variations. Fundamentals of dynamics: Newton, D'Alembert, Lagrange and Hamilton equations of motion. Dynamics of flexible multibody systems: generalized coordinates and generalized Lagrange equations. Applications in robotics and aerospace systems. Bibliography: Meirovitch L, Methods of Analytical Dynamics, McGraw-Hill, New York, 1970; Shabana AA, Dynamics of Multibody Systems, John Wiley & Sons, New York, 1989.

**MP-204: Mechanics of Composite Materials (2004-2007)**Introduction. Fabrication of composite structures. Stress-strain relations. Engineering constants. Classical theory of lamination. Thermal residual stresses. Failure criteria and laminate strength. Experimental characterization. Micromechanics of composites. Laminate strength in the presence of stress concentrations. Bonded joints and mechanical joints. Bibliography: Daniel IM, Ishai O, Engineering Mechanics of Composite Materials, Oxford University Press, Oxford, 1994; Jones RM, Mechanics of Composite Materials, McGraw-Hill, New York, 1975.

**MP-760: Structures I (2004, 2007)**Basic concepts of stress: normal stress, shear stress, arbitrary stress state. Stress and strain under axial loading: strain concept, Hooke's law, Poisson ratio. Stress and strain analysis: stress transformation, principal stresses, failure criteria, arbitrary strain state. Overview of composites: definitions, classifications and fabrication. Euler-Bernoulli beams: pure bending, transverse loading, elastica. Overview of plates. Overview of the finite element method. Bibliography: Beer FP, Johnston ER, Mechanics of Materials, McGraw-Hill, 1982; Megson THG, Aircraft Structures for Engineering Students, London: Edward Arnold, 1990; Chadrupatla TR, Belegundu AD, Introduction to Finite Elements in Engineering, Prentice-Hall, 2002.

**MP-765: Structures II (2005)**Design and sizing: theory of elasticity, stress and strain analysis, introduction to plasticity, failure criteria. Structural analysis: beam theory, plate and shell theory, composite lamina equations, introduction to vibration, modal analysis and dynamic response, introduction to random vibrations. The finite element method: fundamentals, 1D, 2D and 3D elements, solutions of linear systems of algebraic equations. Finite element modeling: geometric modeling, mesh generation, material specification, loadings definition, boundary conditions, static and dynamic analyses. Bibliography: Beer FP, Johnston ER, Mechanics of Materials, McGraw-Hill, 1982; Kraus H, Thin Elastic Shells, Wiley, New York, 1976; Meirovitch L, Elements of Vibration Analysis, 2nd edition, McGraw-Hill, 1986; Chadrupatla TR, Belegundu AD, Introduction to Finite Elements in Engineering, Prentice-Hall, 2002.

**MR-613: Modal Analysis of Structures (2008, 2009)**Introduction. Signal analysis: estimators for frequency response function; review of signal processing (aliasing, leakage and filters, data acquisition boards, signal analyzer, etc.). Analytical formulation - self-adjoint problem: experimental methods applied to 1DOF, orthogonality properties and principle of modal superposition; frequency response function. Analytical formulation - systems with repeated roots: discussion on orthogonality of eigenvectors; generation of modal basis. Practical aspects: systems with pseudo-repeated roots. FRF analysis: real and complex modes; minimum number of measures. Measurement techniques. Data pre-processing. Experiment implementation. Methods for Modal parameter estimation. Pre-processing tools. Operational modal analysis. Bibliography: Edwins DJ, Modal Testing: Theory and Practice, Research Studies Press, John Wiley & Sons, 1995.

**AE-265: Structural Optimization (2008)**General formulation of the optimal design problem. Solution strategies. Structural analysis. Re-analysis. Optimality criteria. Linear and nonlinear programming techniques. Optimization of structural components. Truss optimization. General considerations for large scale optimization problems. Bibliography: Vanderplaats GN, Numerical Optimization Techniques for Engineering Design, Vanderplaats Research and Development, 3rd edition, 1999; Fox RL, Optimization Methods for Engineering Design, Addison-Wesley, 1973.

**MP-230: Computer-aided Analysis of Mechanisms (2002)**Numerical methods for kinematic analysis. Planar kinematics. Computational methods for planar kinematics. Euler parameters. Spatial kinematics. Planar dynamics. Spatial dynamics. Numerical methods for ordinary differential equations. Numerical methods in dynamics. Bibliography: Nikravesh PE, Computer-aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, 1988.

**MP-296: Dynamics of Multibody Systems**Introduction to multibody systems. Kinematics: rotation matrices and their time derivatives, acceleration, Euler angles, direction cosines. Analytical techniques: generalized coordinates and kinematic constraints, virtual work, Lagrange equations, Euler equations. Mechanics of deformable bodies: theory of elasticity, stress and strain, constitutive equations. Classical approximation methods: assumed displacements, generalized coordinates of deformable bodies, velocity and acceleration of material points, kinetic energy, system equations of motion. Finite element formulation: interpolation functions, plane and space systems, viscoelastic and thermoelastic analyses, geometric nonlinearities, composites. Computer implementation: direct numeric integration, dynamic equations in terms of system degrees of freedom, dynamic equations with Lagrange multipliers, partitioning, algorithms. Bibliography: Shabana AA, Dynamics of Multibody Systems, 4th ed., Cambridge University Press, 2013; Nikravesh PE, Computer-aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, 1988; Bauchau OA, Flexible Multibody Dynamics, Springer, Dordrecht, 2011.

### Undergraduate

**EST-11: Introduction to Solid Mechanics (2002, 2008)**Introduction: objectives and methods of solid mechanics. Axial force, shear force, bending moment. Traction, compression and basic elasticity. Stress analysis. Strain analysis. Stress-strain relations. Torsion. Bending of beams. Introduction to energy methods. Introduction to elastic stability. Failure criteria. Bibliography: Popov EP, Introduction to Mechanics of Solids, Prentice-Hall, Englewood-Cliffs, NJ, 1968; Beer FP, Johnston ER, Mechanics of materials, McGraw-Hill, São Paulo, 1982.

**EST-24: Theory of Structures I (2012)**Principles and objectives of the structural analysis. Experimental analysis of stress and strain: strain gauges and optical systems. Work and energy principles: virtual work, total potential energy, reciprocity theorems, unity load theorem. Beams and frames: displacements, resultant forces and moments. The method of forces. Approximate methods: Rayleigh-Ritz. Kirchhoff plates: Navier solution. Bibliography: Allen DH, Haisler WE, Introduction to Aerospace Structural Analysis, New York, John Wiley, 1985; Dally JW, Riley WF, Experimental Stress Analysis, 3rd edition, New York, McGraw-Hill, 1991; Ugural AC, Stresses in Plates and Shells, McGraw-Hill, New York, 1981.

**EST-31: Theory of Structures II (2012)**Torsion of solid sections: Saint-Venant theory. Membrane analogy. Bending and torsion of thin walled beams: open sections, closed sections and multicell; structural idealization. Applications in aeronautical components: wing and fuselage. Stability of bars and beams; exact and approximate solutions. Stability of plates. Bibliography: Megson THG, Aircraft Structures for Engineering Students, 3rd edition, London, E. Arnold, 1999; Curtis HD, Fundamentals of Aircraft Structural Analysis, New York, McGraw-Hill, 1997; Chajes A, Principles of Structural Stability Theory, Englewood Cliffs, Prentice Hall, 1974.

**MPD-42: Mechanical Vibrations (2003-2023)**Single degree of freedom linear systems: free and forced response; harmonic motion of supports, isolation and damping. Periodic and non-periodic excitations: shock spectrum. Two degree of freedom systems: vibration modes, coupling, dynamic absorber. Multi degree of freedom discrete systems: matrix formulation, eigenvalue problems, modal analysis. Continuous systems: beam vibration, approximate methods. Bibliography: Meirovitch L, Principles and Techniques of Vibration. Englewood Cliffs: Prentice Hall, 1996; Inman DJ, Engineering Vibration. 3rd ed., Prentice-Hall, 2007; Rao SS, Vibrações Mecânicas. 4a ed., São Paulo: Pearson Prentice Hall, 2008.

**MPP-33: Computational Techniques for Mechanical Design (2002-2005, 2007, 2008, 2010-2014)**Geometric modeling: 2D and 3D models; curves and surfaces; solid models. Finite element method: basis and applications to elasticity problems and heat transfer. Pre- and post-processing using CAD. Bibliography: Woodwark J, Computing Shape: an Introduction to the Representation of Component and Assembly Geometry for Computer-aided Engineering, ButterWorths, London, 1986.

**MPP-34: Finite Elements (2016, 2018-2023)**Matrices and numerical solution of systems of equations. Fundamental concepts: history, stress and equilibrium, strains, constitutive equations, thermoelastic effect, total potential energy. Rayleigh-Ritz and Galerkin methods. 1D problems: coordinates and interpolation functions, assembly of global matrices. 2D and 3D trusses. Beams and frames: 2D and 3D beam finite element formulation. 2D problems: triangular and axisymmetric elements. Isoparametric elements: 4-noded quadrilateral and numerical integration. Plate elements under bending. 3D solids: tetrahedral and hexahedral elements. Scalar field problems: heat transfer, torsion, potential flow, acoustics. Inviscid compressible flow. Bibliography: Chandrupatla TR, Belegundu AD, Introduction to Finite Elements in Engineering. Prentice-Hall, 3rd edition, 2002; Cook RD, Finite Element Modeling for Stress Analysis. New York: John Wiley, 1995; Reddy JN, An Introduction to the Finite Element Method, McGraw Hill, 1993.

**MTC-51: Introduction to Composite Materials (2002)**Introduction to reinforced materials. Types of fiber and resin. Fabrication processes. Stress and strain transformations. Lamina equations. Ply failure criteria. Classic plate theory. Laminate equations. Laminate failure criteria. Industrial applications and characterization. Bibliography: Daniel IM, Ishai O, Engineering Mechanics of Composite Materials, Oxford University Press, 1994; Jones RM, Mechanics of composite materials, McGraw-Hill, New York, 1975.