TO INTEGRATE AND TO COMPLETE THE STUDENTS KNOWLEDGE IN STRUCTURAL DYNAMICS, FOCUSING ON SPECIFIC PROBLEMS OF AIRCRAFT STRUCTURES AND ON NUMERICAL METHODS WIDELY USED FOR THEIR ANALYSIS. IN PARTICULAR, THE EMPHASIS WILL BE PLACED ON LINEAR AND NON-LINEAR MODELING OF AIRCRAFT STRUCTURES SUBJECT TO THE COMBINED ACTION OF THERMAL AND EXTERNAL LOADS. IN A FIRST STAGE, THE THEORY NECESSARY FOR THE MODELING OF SPECIFIC AIRCRAFT STRUCTURES PROBLEMS WILL BE PRESENTED AND THE BASIC THEORY OF FINITE ELEMENT METHODS WILL BE PROVIDED, WITH PARTICULAR ATTENTION TO AERONAUTICAL APPLICATIONS. IN A SECOND STAGE, THE STUDENT WILL BECOME FAMILIAR WITH FINITE ELEMENT CODES COMMONLY USED FOR STRUCTURAL DESIGN IN INDUSTRIES. THIS ACTIVITY WILL BE AIMED AT THE STRUCTURAL ANALYSIS OF ONE OF THE MOST IMPORTANT ELEMENTS OF THE AIRCRAFT (WING AND/OR FUSELAGE).
teacher profile teaching materials
The teaching program is structured to provide students with knowledge and skills in the structural design of aeronautical components, using methods widely used in the aircraft detailed design phase.
The teaching program is divided into 36 lectures (equal to 9 CFU) divided into the following eight main sections:
1) Tensor Calculus Fundamentals: N-th order tensors. Tensor operations. Curvilinear coordinates. Covariant and contravariant base vectors. Vectors and tensors in curvilinear coordinates. Differential operators in curvilinear coordinates.
2) Kinematics of Deformable Continua: Lagrangian and Eulerian descriptions of motion. Finite strain theory. Displacement and deformation gradient tensors. Polar decomposition theorem. Lagrangian and Eulerian finite strain tensors (Cauchy-Green and Eulero-Almansi). Rates of deformation tensors. Linearization of the finite strain theory (infinitesimal strain theory). Material and spatial descriptions of the continuity equation.
3) Dynamics of Deformable Continua: Material and spatial forms of linear momentum balance, Cauchy's theorem. Cauchy and Piola-Kirchhoff stress tensors. Material and spatial forms of the angular momentum balance. Material and spatial forms of the mechanical energy balance.
4) Thermodynamics of Deformable Continua: Material and spatial forms of the energy balance. Stokes' heat flux theorem. Material and spatial forms of the thermodynamic energy balance. The second law of thermodynamics.
5) Constitutive relations theory: Noll's axioms. Limitations on the constitutive relations due to the second law of thermodynamics. Constitutive relations for thermoelastic materials: definition of isothermal elastic tensor, thermal stress tensor, and thermal conductivity tensor. Constitutive equation for linear isotropic thermoelastic materials.
6) Thermoelastic problems in aeronautical structures: Uncoupled thermoelastic formulation. Initial boundary value problem of the heat conduction equation. Thermal stress analysis for elastic bodies subjected to external and thermal loads: Euler-Bernoulli beam and Kirchhoff plate.
7) Finite Element method: Strong and weak forms of the uncoupled thermoelastic problem. The relation between strong and weak forms and boundary conditions. Virtual work principle. Discretization and definition of shape functions. Shape function choice criteria. Evaluation of element mass, stiffness and damping matrices. Evaluation of equivalent nodal loads vector. Assembly procedure. The imposition of displacement constraints. Conformal elements. Non-conformal elements – patch test. Isoparametric elements. Standard methods for shape functions construction. Applications in aeronautical problems: truss, beam, plate, and shell.
8) Introduction to the code Autodesk Inventor: Geometric preprocessor. Material properties definition. Constraints and external loads imposition. Solution methods. Post-processing. Structural analysis of a wing and/or a fuselage.
- Boley, B.A, Weiner. J.H., Theory of Thermal Stresses, John Wiley & Sons, New York, 1960 (for contents 4, 5 and 6 of the syllabus)
- Thomas J.R., Hughes, ‘The Finite Element Method – Linear Static and Dynamic Finite Element Analysis,’ Dover, 2000 (for content 7 of the syllabus)
- T.H.G., Megson, Aircraft Structures for Engineering Students, Arnold, London, 1999 (for content 7 of the syllabus)
- Lectures notes by the teacher (for all the contents of the syllabus)
The educational material used by the teacher from time to time is indicated during lectures. The lecture notes are made available on the Moodle platform to facilitate their use for both attending and non-attending students. On the same platform, are also made available the specifications of the project the students have to perform during the year, as well as a collection of written tests of previous exams, to provide students with a valid and realistic test bench for the final exam.
Programme
The Analysis of Aeronautical Structures course is part of the activities of the Constructions and aerospace structures (ING-IND/04 SSD).The teaching program is structured to provide students with knowledge and skills in the structural design of aeronautical components, using methods widely used in the aircraft detailed design phase.
The teaching program is divided into 36 lectures (equal to 9 CFU) divided into the following eight main sections:
1) Tensor Calculus Fundamentals: N-th order tensors. Tensor operations. Curvilinear coordinates. Covariant and contravariant base vectors. Vectors and tensors in curvilinear coordinates. Differential operators in curvilinear coordinates.
2) Kinematics of Deformable Continua: Lagrangian and Eulerian descriptions of motion. Finite strain theory. Displacement and deformation gradient tensors. Polar decomposition theorem. Lagrangian and Eulerian finite strain tensors (Cauchy-Green and Eulero-Almansi). Rates of deformation tensors. Linearization of the finite strain theory (infinitesimal strain theory). Material and spatial descriptions of the continuity equation.
3) Dynamics of Deformable Continua: Material and spatial forms of linear momentum balance, Cauchy's theorem. Cauchy and Piola-Kirchhoff stress tensors. Material and spatial forms of the angular momentum balance. Material and spatial forms of the mechanical energy balance.
4) Thermodynamics of Deformable Continua: Material and spatial forms of the energy balance. Stokes' heat flux theorem. Material and spatial forms of the thermodynamic energy balance. The second law of thermodynamics.
5) Constitutive relations theory: Noll's axioms. Limitations on the constitutive relations due to the second law of thermodynamics. Constitutive relations for thermoelastic materials: definition of isothermal elastic tensor, thermal stress tensor, and thermal conductivity tensor. Constitutive equation for linear isotropic thermoelastic materials.
6) Thermoelastic problems in aeronautical structures: Uncoupled thermoelastic formulation. Initial boundary value problem of the heat conduction equation. Thermal stress analysis for elastic bodies subjected to external and thermal loads: Euler-Bernoulli beam and Kirchhoff plate.
7) Finite Element method: Strong and weak forms of the uncoupled thermoelastic problem. The relation between strong and weak forms and boundary conditions. Virtual work principle. Discretization and definition of shape functions. Shape function choice criteria. Evaluation of element mass, stiffness and damping matrices. Evaluation of equivalent nodal loads vector. Assembly procedure. The imposition of displacement constraints. Conformal elements. Non-conformal elements – patch test. Isoparametric elements. Standard methods for shape functions construction. Applications in aeronautical problems: truss, beam, plate, and shell.
8) Introduction to the code Autodesk Inventor: Geometric preprocessor. Material properties definition. Constraints and external loads imposition. Solution methods. Post-processing. Structural analysis of a wing and/or a fuselage.
Core Documentation
- M.E., Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981 (for contents 1, 2, 3 and 5 of the syllabus)- Boley, B.A, Weiner. J.H., Theory of Thermal Stresses, John Wiley & Sons, New York, 1960 (for contents 4, 5 and 6 of the syllabus)
- Thomas J.R., Hughes, ‘The Finite Element Method – Linear Static and Dynamic Finite Element Analysis,’ Dover, 2000 (for content 7 of the syllabus)
- T.H.G., Megson, Aircraft Structures for Engineering Students, Arnold, London, 1999 (for content 7 of the syllabus)
- Lectures notes by the teacher (for all the contents of the syllabus)
The educational material used by the teacher from time to time is indicated during lectures. The lecture notes are made available on the Moodle platform to facilitate their use for both attending and non-attending students. On the same platform, are also made available the specifications of the project the students have to perform during the year, as well as a collection of written tests of previous exams, to provide students with a valid and realistic test bench for the final exam.
Type of delivery of the course
The teaching is structured in 36 class lectures. Some classes are devoted to practical deepening the theoretical arguments, through appropriate tutorials led by the teacher. Some classes are also dedicated to the presentation of the code Autodesk Inventor, which will be used for the project that has to be carried out as group work by the students and presented at the final exam. The educational material is made available on the Moodle platform, to facilitate its use for both attending and non-attending students.Attendance
Class attendance, although recommended, is not mandatory.Type of evaluation
Students' learning is assessed through a written test of 2 hours and a half, and an oral test. The written test includes an exercise and one or two theoretical questions with open answers, aimed at verifying the level of effective understanding of the concepts and the students' ability to apply them in real contexts. Passing the test is the prerequisite to participate in the oral test, which includes theoretical and practical questions related to the entire program. During the oral test, the group project that the students carried out during the year will also be discussed. During the COVID-19 emergency period, the evaluation activities will be carried out according to Article 1 of the Rectoral Decree n. 703 of 5 May 2020.