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- To be admitted at ULiège (Liege) - Master 1:
Existing background in the following fields are expected. The mentionned lectures are only given as exemples. Your lectures may have different names and content.
• Fundamental branches:
o Mathematics and Numerical Analysis
o Physics, Thermodynamics
• Solid mechanics, 5 credits (or equivalent) (see (*) )
• Strength of materials, 5 credits (or equivalent) (see (**) )
• Fluid mechanics, 5 cr, (or equivalent) (see (***) )
• Heat transfer, 5 credits (or equivalent)
• Dynamics of mechanical systems, 5 credits (or equivalent)
• Experience in programming, Finite Element Method, Programing code and CAD
- Programming (coding), using for instance MATLAB, C++, Python, …
- Finite Element Method : appreciated but not mandatory
- CAD tool is highly relevant (but not mandatory)
- To be admitted in URO (Rostock) - Master 2: You need to have completed 18 ECTS of Mechanics, 18 ECTS of Mathematics, 12 ECTS of fluid mechanics, 6 ECTS of Measurement Technology / Control Engineering (or equivalent lectures).
- To be admitted in ECN (Nantes) - Master 2: Candidates need to have completed lectures in Mathematics and Fluid Mechanics, which is verified through the admission procedure to enter at Master 1 at ULiège.
- To be admitted at UPM (Spain) - Master 2: Candidates need to have succeeded the Master M1 at ULiège
(*) Solid mechanics
Overview and structure of the course
• General equilibrium principles (identification of all external efforts acting on the studied body, concept of the cut and identification of the internal forces acting on both sides of the cut)
• Notions of stresses and of plasticity surfaces (Mohr circle in in-plane stress field)
• Material properties: link between the stresses and the deformations
• Beam definition
• Calculation of internal forces in a structure constituted of beams (MNT diagrams)
• Calculation of internal forces in a truss
• Study of the different internal forces in a beam section - how to pass from forces to stresses (tension, compression, bending, torsion, shear, combined loading)
• Deflections in structures made of beams
• Concept of second order analysis and notions of elastic buckling of beams in compression
(**) Mechanics of materials
This course provides the basic knowledge in Solid Mechanics: concept of stress tensor, strain tensor, material's constitutive law, Hooke's law, deformation energy and link with thermodynamics, virtual work principle and energy theorems, isotropic linear elasticity theory. These concepts are then applied to various practical cases: thick tubes under pressure, pressurized sphere, force on an infinite medium, contact between two elastic solids, torsion of prismatic solids, tensile and bending of prismatic solids, corner shaped solids, stress concentration...
The topics of the course are: * Introduction to tensorial calculus and index notation. Application to the statics: stress tensor, balance equations... * Kinematics: strain in 1D, rigid body motion, tensoriel definition, F=RU, Saint-Venant compatibility equations * Virtual work principle + energy theorems (Engesser, Castigliano...) * 3D Hooke's law, material mechanical properties, additivity rule, strain energy, uniqueness of the solution * Fundamental equations of linear elasticity (Navier's equations) * 3D elastic problems: pressurized tubes, pressurized sphere, Boussinesq's problem, Hertz contact problem * Torsion of general prismatic solid: warping of the sections... * 2D elastic problems: applications in cartesian coordinates (tensile and bending of prismatic solids) * 2D elastic problems: applications in polar coordinates (bending of a curved beam, corner shaped solids, plate with a hole, stress concentration) * Fatigue: introduction to the concept of fatigue, origin of fatigue failure, Wöhler curves, number of cycle to failure, endurance limit.
(***) Fluid mechanics
Course contents :
The course provides a rigorous and systematic presentation of the basic concepts and classical mathematical models used in various fields of application of Newtonian fluid mechanics. These models, and their simplified versions, are used to better understand the underlying physical processes.
The following topics are addressed:
• Kinematics of fluid flows.
• Budget equations (local and integral forms) and associated boundary conditions. Newtonian fluid and Navier-Stokes equations.
• Vorticity dynamics and potential flow.
• Similitude theory and flow regimes.
• Introduction to gas dynamics : rule of forbidden signals in supersonic flows, shock waves.
• Turbulence : characterization, RANS simulations, Taylor theory of turbulent dispersion.
• Gravity waves, capillarity waves, internal waves
Learning outcomes of the course :
At the end of the course, the student will master the basic concept of Newtonian fluid dynamics. He/She will be able to use both the tensor and indicial formalism to design mathematical models of most large scale and small scale flows. In particular, he/she will be able to make the link between the physical processes and their mathematical parameterization and to justify the main assumptions.
He/She will be able to write down budget equations, understand the processes responsible for the transport of information and energy in fluids, use integral forms of the Navier-Stokes equation to describe simple flows. He/She will also be able to rely on a simplified 1D model to describe shock waves in a nozzle.
Through the group project, the course contributes to the development of soft skills like self-study, collaborative work and reporting.