Aerospace engineering

0. Introductory concepts of solid mechanics for design 0.a Strength and stiffness parameters  Main stresses (and main directions)  Maximum cuts and relationships with the main stresses  Linear constitutive bonds with engineering constants (elementary mono-axial and shear tests) for the elastic compliance matrix: orthotropic and isotropic case  Elastic energy of deformation: constraints  Plane elasticity: state of plane deformation and plane stress (discussion on the use of plane stress)  Floor problem solutions with Airy function (extra) 0.b Strength criteria  Strength criteria for brittle materials: maximum criterion of the main stresses, Coulomb criterion  Yield criteria for ductile materials: Tresca yield criterion, Von Mises criterion  Outline of Fracture Mechanics (extra) 1. Environment and functionality of Aerospace structures 1.a Loads and loading environments  Static, quasi-static and dynamic loads. Load factor, load terminology and coefficients and safety margins in projects. Fatigue  Aircraft: mechanical environment on an aircraft and maneuver diagram Launchers: Typical weights, loads (transport and launch) and flight profiles Satellites: Payload, carriage, systems, importance of launcher type (loading environment), solar panels 1.b Elements and functionality of aerospace structures and materials  Basic structural elements of Aeronautical structures (axial members, panels, flexural and torsional members)  Wings and fuselage: load transfers and functionality  Aviation materials: 5 properties for metallic and composite materials (PMC, CMC and MMC) 2.TORSION of long structures: generic solid and thin-walled sections (torsional shear stress) - The Saint-Venant's principle for the aeronautical half-shell - Torsion of uniform bars (kinematic hypotheses and Prandtl function) - Solid sections: a) circular case b) case with narrow rectangular section. Torsional stiffness - Single-cell and multi-cell thin-walled sections. Torsional stiffness - Primary bulging in open and closed sections. Hitching prevented (extra) 3.The BENDING of long structures and shear stress of a bending nature in the open sections - Euler-bernoulli beam: bending in the plane and in space. Principal axes and neutral axes of bending - Practical problems of the bent Kirchhoff beam analytically solved (2nd and 4th order) - The shear stress of a bending nature in rectangular and generally symmetrical thin walls (Cartesian coordinates) and relative shear deformation (first differentiations with the simple beam theory) - Notes on the Timoshenko beam (extra) - Notes on shear lag (Saint-Venant's) for flexion problems (extra) 4. Stress and shear flows of a flexural and torsional nature in thin-walled sections: the aeronautical wing-box - Bending shear stress for open thin-walled structures (coord-curvilinear): symmetrical sections (case with section that absorbs normal stress and simplification of stringers) and general case of non-symmetrical sections. Nodal junctions. Cut center in open sections - Flexural and torsional shear stress for closed thin-walled structures: the aeronautical half-shell single-cell thin-walled closed sections: combination of flexural and torsional shear stress. Determination of the cutting flows and the cutting center (particular case of statically determined structures) closed sections with multicellular thin walls. Determination of the cutting flows and the cutting center 5. Energy approach and approximate methods of spatial discretization in structures (Galerkin, Rayleigh-Ritz) Space-discrete mechanical systems: - The equations of motion for the particle scheme of material points and its "weak formulation" (law of virtual works) - Constraints on motion and Lagrangian formulation: Lagrange equations of motion - The Lagrange equations of motion with linear link between motion variables and Lagrangian variables: the mass matrix and its algebraic properties. Elastic elements and the stiffness matrix. Examples - Necessary and sufficient condition which must satisfy an equilibrium solution (static) in physical or Lagrangian variables for a system subject to conservative forces only - Conservation over time of total energy (Hamiltonian) in the presence of conservative forces: case of generic Lagrange variables and case in which the motion unknowns linearly depend on them Space-continuous mechanical systems: - Elastic energy possessed by a solid linear space-continuum and energy of conservative loads: one-dimensional case of a rod-beam. The total energy functional (elastic plus conservative loads) - Necessary and sufficient condition that must satisfy an equilibrium solution (static) in physical variables for a continuous space system subject to conservative forces only Functionals and stationarity conditions of functionals to an independent variable of order 1 and 2 (member and beam): generation of equilibrium equations and natural boundary conditions - "Strong formulation" of the linear elastic linear problem with the displacement method (generalized 3D problem, member, beam) and "weak formulation" - Introduction of the (infinite) Lagrangian variables in linearized form only (between physical and Lagrangian variables) and related shape functions. Obtaining the (infinite) Lagrange equations by projection. Discretization of a continuous space mechanical system: - Truncation of variables and Lagrange equations: the Galerkin method - the Finite Element method as a Galerkin method with "hat functions" - The stationary condition of the static solution for a continuous space system for a discretized system: the Rayleigh-Ritz method. Equivalence with Galerkin's method. Examples 6. Structural Dynamics of N-DOF systems: discrete or discretized - Eigenvalue problem associated with a space-discrete / discretized mechanical system and its spectral properties (three spectrum theorems). - Free system response. Physical concept of proper mode of vibration and natural frequency of vibration  Forced response problems over time with the modal technique - The typical aeronautical wing section (bending-tosion couplings) - Notes on the description in the frequency domain and response to permanent harmonic regime (extra) 7. Structural collapse (global): stability of the elastic equilibrium General concept of stability of solutions over time and equilibrium solutions, dynamic and energetic method. Stability of the equilibrium of spatially discrete or discretized systems (ODE) 1DOF: - The DYNAMIC / STATIC METHOD: basic equation, solution, equilibrium, linearization, solution and critical parameter. - The ENERGY METHOD: total elastic energy and conservative load, stationarity and verification of the minimum. Stability of the equilibrium of spatially discrete or discretized systems (ODE) 2DOF and N DOF: - The DYNAMIC / STATIC METHOD: linear equations on a system with conservative load, solution around the trivial equilibrium position, determination of the critical load and of the critical deformation. - The ENERGY METHOD: the minimum condition of the total energy (elastic and conservative load) as a condition on the real eigenvalues of the Hessian matrix - that is, the total stiffness matrix -: determination of the critical load and critical deformation. Stability of the equilibrium of spatially continuous systems (PDE): Euler-Bernoulli beam - Equations of the Euler Bernoulli beam with axial load (conservative) with equilibrium on the deformed configuration. - The lesson learned from discrete systems in the case of conservative loads with the DYNAMIC and ENERGETIC methods: find the conditions that make the trivial / null solution indeterminate as the peak load increases. - Case studies of critical load and limit critical deformation for a press-compressed Euler-Bernoulli beam: i) C.C. double support; ii) C.C. free clamped; iii) C.C. clamped supported; iv) C.C. clamped clamped. Effective lengths and slenderness of a beam with buckling.

Prerequisites of the course are knowledge of solid continuum mechanics, simplified one-dimensional structures (Euler-Bernulli beam and member model).

C.T. Sun: "Mechanics of Aircraft Structures", John Wiley & Sons, Inc., second edition, 2006. Further teaching material is provided by the teacher during the course.

The course is held with traditional frontal lessons (with further parallel remote connection in a pandemic emergency) both for the more theoretical aspects and in carrying out practical and design exercises.

Attendance of the face-to-face course is strongly recommended.

The assessment of the acquired knowledge is carried out with a final written test on theoretical questions and exercises of practical applications of the acquired knowledge on exemplary cases of aerospace structures. A subsequent oral test is on demand by the student.

The course is held with traditional frontal lessons (with further parallel remote connection in a pandemic emergency) both for the more theoretical aspects and in carrying out practical and design exercises.

See the content proposed for the same section by the course tenant prof. Franco Mastroddi.

See the content proposed for the same section by the course tenant prof. Franco Mastroddi.

See the content proposed for the same section by the course tenant prof. Franco Mastroddi.

See the content proposed for the same section by the course tenant prof. Franco Mastroddi.

See the content proposed for the same section by the course tenant prof. Franco Mastroddi.