M1 Mechanics - International track

Andrea Barbarulo Filippo Gatti Pierre Jehel.

Typical 1h30 lectures followed by 1h30 tutorial classes, except for sessions 6, 10 and 11 (3h-sessions of tutorial classes) Overall grade 20% intermediary examination 1 grade + 20% intermediary examination 2 grade + 60% final examination grade Exam: All paper documents allowed, as well as non communicating calculators.

1. Strains: Lagrangian description of movements, Green-Lagrange strain tensor, infinitesimal strain tensor
2. Stresses: global equilibrium equations for a material medium, Cauchy stress tensor, local equilibrium equation
3. Strength criteria: mechanical tests, brittle fracture criteria, Tresca and von Mises criteria, stress concentrations
4. Material behaviour: diversity, linear elastic isotropic behaviour, thermoelasticity
5. Elasticity: properties of the mechanical solution, exact and approximate solutions, simplifications of an elastic problem
6. Intermediary examination 1 (MCQ of 45 min) + numerical session 1:
tutorial session about the software Comsol Multiphysics on a simple example
7. Beam approximation: approximate kinematics, definition of the internal loadings + numerical session 2: demonstration of the assumptions of the beam model
8. Beam approximation: constitutive relations, connections
9. Beam approximation: solution methods
10. Intermediary examination 2 (MCQ of 45 min) + summary problem on beams
11. Summary session: analytical and numerical solution of a continuum mechanics problem.

None.

Lecture notes.

Septembre - Octobre.

GIF-SUR-YVETTE

11 course sessions: 3h00 each (1h30 of lecture followed by 1h30 of practice session) 2 homework projects during the first part of the course: 3h00 are scheduled during the course for supervision. Possible visit during the thematic block #3 3 evaluations associated to the different blocks: Block #1 (25%): 2 homework projects Block #2 (50 %) : written exam scheduled during the last session Block #3 (25%): poster preparation and presentation.

Block #1: Advanced Fluid Mechanics (4 sessions)
- Local transport equations and global balances: reminders, vector and conservative forms of the equations
- Theoretical approaches to determine analytical solutions: selfsimilarity, stream function, potential flows.
- Characterization and conception of a system from global balance equations.
- Handling of numerical and experimental data. Numerical tools and experimental diagnostics for flow field characterization.
- Unsteadiness and flow instabilities
- Signal processing applied to the analysis of unsteady flows.
Block #2: Compressible flows (4 sessions)
- Isentropic flows with variable cross-section
- Stagnation and critical conditions, isentropic efficiencies, turbines and compressors
- Normal and oblique shock wave
- Nozzle regimes
Block #3: Thematic sneak peek (three sessions)
- Choice between different themes such as Aerodynamics, Meteorological and climatic flows, Aeronautical and space propulsion, Energy systems...

Fundamental concepts and skills in fluid mechanics: - Dimensional analysis - Local and macroscopic balance equations for mass, species, momentum and energy - Evolution of different fields (velocity, pressure, temperature) and their interactions - Determination of stresses, forces, powers, efficiencies, head losses - Boundary layer.

GIF-SUR-YVETTE

A placement test will determine the level of the course: B1, B2, or C1 (European reference framework) The evaluation is organized in two ways: continuous assessment and control of the end of half-year.

Those weekly courses are offered at several levels, depending on the results
of the placement test. Classes are organized as practical workshops focusing
on oral understanding and communication, written understanding and
communication, structural proficiency (grammar, vocabulary). Students will
work individually or in groups on themes related to contemporary French
culture in relation to its historical past.

B1 level in French.

Specific to each course and group level: printed documents (press, literature), audio/video (films, recordings), textbooks.

Octobre - Novembre - Décembre - Janvier.

GIF-SUR-YVETTE

S1 to S5: Lectures + tutorial classes S6: Hands-on sessions: groups of 4 S7 to S10: Lectures + tutorial classes S11: Paper analysis by groups of 2 2-hr written exam (coeff 0.7) + analysis of a scientific paper (coeff 0.3).

1. Introduction to vibration: discrete Multi Degree of Freedom (MDOF) systems
2. Beam Theory (Euler-Bernoulli) Application to beam dynamics and vibration
3. Virtual Power Principle on 3D and beams applications
4. Finite Elements for Dynamic problems- Dynamic response
5. Dynamic response to random loads
6. Hands-on session: Comsol FE modeling of a building under seismic and wind excitation
7. Acoustics 1: equations and basic sources (monopoles, dipoles )
8. Acoustics 2: Waveguides and applications
9. Acoustics 3: Acoustic modes in bounded domains
10. Wave propagation in infinite media (Soils, acoustics in presence of wind or temperature gradients).

Continuum mechanics.

Lecture notes.

GIF-SUR-YVETTE

Gabi Stancu.

Eleven 3-hour sessions are scheduled. A Continuous Exam (CE) grade is determined by evaluating the students through three very short tests that are prepared beforehand and treated in class without any printed documents. A Final Exam (FE) grade is determined though a 2h00-long written exam where printed documents are allowed. The final grade obtained for the course is computed as the maximum between: The final exam grade FE only, The weighted grade 0.33xCE + 0.67xFE.

RADIATIVE HEAT TRANSFER
Conduction, convection, radiation. 1st energy balance equation. Analogy.
Opaque body / transparent medium. Fluxes. Spectral directional intensity. Equilibrium.
RADIATIVE PROPERTIES AND TRANSFER
Emissivity, absorptivity and reflectivity. Grey, black and diffuse body.
FLUID FLOW
Theorem Pi. Motion, material derivative. Velocity. Acceleration. Local balance of mass. Mixtures.
SPECIES MASS TRANSFER
Local balance. Velocities. Heat / mass transfer analogy. Fick’s law. Mass diffusivity. A-priori approximations. Characteristic scales.
BALANCE OF MOMENTUM
General motion of a particle. Stress-strain rate relation. Local balance equation of momentum / kinetic energy. Euler / Navier-Stokes equations. Dimensional analysis.
ENERGY BALANCE
Local / macroscopic balance. Transport for mass, concentrations, momentum, energy. Bernoulli theorem. Incompressible flows. Head losses. Moody diagram. Pump and turbine efficiency.
MACROSCOPIC BALANCE
Mass / species / thermal energy. Momentum, moment of momentum. Thrust of turbo-engines and rockets.
PHYSICS OF BOUNDARY LAYER
A-priori estimates. Separation, transition. Thicknesses, equations, numerical solutions.
EXTERNAL FORCED CONVECTION, MECHANICAL / THERMAL BOUNDARY LAYER
Integral method. Pressure. Correlation formula for external forced convection. Simplifications.
INTERNAL FORCED CONVECTION
Mechanical / thermal entrance zones and regimes. Bulk velocity / temperature. Velocity profile in laminar regime. Nusselt number. Hydraulic diameter.

Basics of mathematics and thermodynamics (studied during the first 2 university years).

Provided course material Polycopié CentraleSupélec « Mécanique des Fluides» ; Tome I ; Sébastien Candel. « Transferts thermiques - Introduction aux transferts d’énergie » ; 5e édition ; auteurs : Jean Taine, Franck Enguehard et Estelle Iacona ; Dunod, Paris, 2014.

Septembre - Octobre.

GIF-SUR-YVETTE

Gabi Stancu.

Eleven 3-hour sessions are scheduled. A Continuous Exam (CE) grade is determined by evaluating the students through three very short tests that are prepared beforehand and treated in class without any printed documents. A Final Exam (FE) grade is determined though a 2h00-long written exam where printed documents are allowed. The final grade obtained for the course is computed as the maximum between: The final exam grade FE only, The weighted grade 0.33xCE + 0.67xFE.

HEAT TRANSFER
Wall between two fluids; Temperature profile in a 1Dsystem; Insulation of a cryogenic container
FIN AND FIN APPROXIMATION
Heated plate; Cooling of an electronic circuit; Efficiency of an home radiator; Liquid temperature measurement - glove finger
THERMAL RADIATION
Calculations of solid angles and fluxes; Spectral integral calculations of Planck's law; Principle of IR remote sensing of a body
RADIATIVE PROPERTIES AND TRANSFER
Radiation between two spheres; Temperature of a body exposed to solar radiation
GENERAL METHOD OF RADIATIVE TRANSFER BETWEEN OPAQUE BODIES IN TRANSPARENT ENVIRONMENT
Radiation « face to face »; Radiative screen - temperature measurement by a thermocouple
UNSTEADY DIFFUSION: HEAT CONDUCTION
Modeling of a 2D unsteady conduction problem; 1D unsteady conduction - analytical solution in case of imposed flux; Thermal inertia of a building; Cooling of a transparent ball; Laser treatment of steel
PHENOMENOLOGICAL APPROACH OF EXTERNAL FORCED CONVECTION
Bay window on forced external convection; Conductor, prudence!
INTERNAL FORCED CONVECTION
Calculation of the transfer coefficient in a semicircular channel; Helium as a heat-exchanging fluid; Circulation of water in a tube (home work)
DIMENSIONAL ANALYSIS OF NATURAL CONVECTION
Thermal study of double glazing
SYNTHESIS: Energy recovery for residential tertiary; Air conditioning of a building in a hot and sunny region.

Basics of mathematics and thermodynamics (studied during the first 2 university years).

- « A first course in heat transfer » J. Taine, E. Iacona, Editions Dunod 2011. - « Transferts Thermiques » Partie 1, J. Taine, F. Enguehard, E. Iacona, Dunod 2014. - Platform « E-Self-Learning: http://e-mentor-en.ecp.fr/ presented by G.D. Stancu. - Platf.

Novembre - Décembre.

GIF-SUR-YVETTE

Maria Vakalopoulou.

- Lectures (12 sessions x 1h30) - Labs (10 sessions x 1h30) - Written exam (2 hours) The evaluation of the course will be based on the following: Two assignments: the assignments will include theoretical questions as well hands-on practical questions that.

Introduction to Machine Learning
Dimensionality reduction
Model selection and evaluation
Linear and logistic regression
Probabilistic classifiers and linear discriminant analysis
Non-parametric learning and nearest neighbour methods
Tree-based methods and ensemble learning
Support Vector Machines
Neural networks
Unsupervised learning: clustering
Introduction to reinforcement learning.

Notions of linear algebra, probabilities, and scientific programming in Python (numpy).

- Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, 2014. - Christopher M. Bishop. Pattern Recognition and Machine Learning. Springer, 2011. - Trevor Hastie, Robert Tibshirani, a.

Novembre - Décembre.

GIF-SUR-YVETTE

Camille Gandiolle.

Sessions 1 to 6: lecture + directed study session - Session 7: working session - Sessions 8 and 9: lecture + directed study session - Sessions 10 and 11: working session The final case study allows to evaluate learning outcomes #1, 4 and 5, whereas the exam gives the opportunity to evaluate learning outcomes #1, 2, 3 and 4. Every learning outcome is evaluated separately. A feed-back is given to the students on the skills they have developed.

1. Introduction, approach of modelling: Case study on a thermal-elasticity problem (recalls)
2. Anisotropic elasticity of composite materials: Introduction to composite materials (nature, interest using Ashby maps, manufacturing process). Anisotropic linear elasticity. Calculation of the properties of the equivalent
homogeneous medium.
3. Homogenization of heterogenous materials: Homogenization scheme. Voigt and Reuss bounds.
4. Polymer and elastomer viscoelasticity: Introduction to polymers (nature, behavior with respect to temperature). Viscoelasticity. Time dependent behavior.
5. Mechanisms of plasticity in metallic alloys: Structure and defects of crystalline materials. Dislocations and Schmid factor. Hardening of alloys.
6. Elastoplasticity: Description of elastic domain changes. Strain decomposition. Incremental 3D elastoplasticity.
7. Case study: choice of a model. (On 2 given cases, analyze the problem, propose/create a model able to account for the physical mechanisms observed.)
8. Identification of constitutive laws: introduction to optimization (objective function, sensitivity, minimization)
9. Safety of structures - damage and fracture: introduction to concrete (nature and specificities in behavior and damage). Volume damage. Crack sustainability.
10. Case study (use of the various concepts of the course on a given application)
11. Case study(use of the various concepts of the course on a given application).

Continuum mechanics or Materials Model representations and analysis.

Chaboche and Lemaître, Mechanics of Materials, Dunod Roesler, Harders, Baeker, Mechanical Behaviour of Engineering Materials, Springer, 2007 Besson, Cailletaud, Chaboche, Forest, Non linear Mechanics of Materials, Hermès, 2001.

Novembre - Décembre.

GIF-SUR-YVETTE

A placement test will determine the level of the course: B1, B2, or C1 (European reference framework) The evaluation is organized in two ways: continuous assessment and control of the end of half-year.

Those weekly courses are offered at several levels, depending on the results of the placement test. Classes are organized as practical workshops focusing on oral understanding and communication, written understanding and
communication, structural proficiency (grammar, vocabulary). Students will work individually or in groups on themes related to contemporary French culture in relation to its historical past.

B1 level in French.

Specific to each course and group level: printed documents (press, literature), audio/video (films, recordings), textbooks.

Février - Mars - Avril - Mai.

GIF-SUR-YVETTE

Frédérique Laurent-Nègre.

Classical Lectures, Tutorial, Projects Written exam, oral exam, Project 1st session: Written exam (coef 2), Project (coef 1) 2nd session: Oral or written exam.

The course is composed of two successive parts of 5,5 x 3h, each.
1. Compressible fluid flows simulation :
- Flow models, discontinuous solutions, Entropy, Basic solvers, extensions
- Practical implementation
2. Modeling, mathematical analysis and controlled simulation in solid mechanics
-Derivation of linear elasticity equations: strong and weak forms
-Mathematical analysis of the primal weak problem. Vectoriel Finite element approximation. A priori error estimation
-Practical implementation and approximation of a singular problem (as mini-project).

Mechanical Fields for Solids and Fluids-basic governing equations and meaning of these equations Basic notions of differentiation and integration Basic notions on Hilbert spaces and weak formulations of PDEs Basic notions on stability and prime notions on space and time approximation schemes for PDEs. Roughly speaking : a first year CS level of knowledge in Mathematics and Mechanics or a 3rd University year in Applied Mathematics to Mechanics.

Handout PDEs (first CS year) and Handouts for the two parts (Fluid and Solid) of the course (and references therein).

Avril - Mai.

GIF-SUR-YVETTE

Guillaume Puel.

S1 to S9 : lecture 1h30 + numerical projet on Comsol 1h30 S10 to S11 : Hands-on sessions: MEMS design in groups of 4 2-hr written exam (1 theory + 1 on simulation tool): 65% of the final score Project evaluation: 35% of the final score.

S1-S2 Variational formulation and 1D FEM
Project: Beam (Mechanics)
S3-S4 2D FEM
Project: Heated room with open window (Weak coupling Thermic and Fluid Mechanics)
S5 Multiphysic coupling techniques
Application: Lift force of a slender body (Full coupling Thermic, Fluid mechanics, mechanics)
S6-S7 Model error estimation
Project: Heated room with open window (Error estimation)
S8-S9 Time and frequency dependent problems
Project: Electromagnetic compatibility in a room (Electromagnetic wave dynamic and Transmission liner).

Partial Differential Equations Electromagnetism or Materials or Continuum mechanics or Introduction to mass, momentum and heat transfer.

None.

Avril - Mai.

GIF-SUR-YVETTE

This course combines lectures and exercise/practical classes The grading will be based on a continuous evaluation process (1/3 of the final grade) and the final written exam (2/3 of the final grade). In case of a justified absence to one of the intermediary examinations, the grade of this latter is replaced by the grade of the final examination.

1. Optimization basics
1.1 Introductory notions
1.2 Existence of minimizers
1.3 Convexity
1.4 Duality
2. Linear programming
3. Integer linear programming
4. More advanced notions in continuous optimization
4.1 Lagrange multipliers method
4.2 Some iterative algorithms.

Basics in functional analysis and probability, knowledge of a programming environment.

D. P. Bertsekas, Nonlinear Programming, 3rd Edition. Athena Scientific, 2016. ISBN:978-1-886529-05-2 H.H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd Edition. Springer, 2017. ISBN: 978-3-319-48311-5.

Février - Mars.

GIF-SUR-YVETTE

Février - Mars.

GIF-SUR-YVETTE

Avril - Mai.

GIF-SUR-YVETTE

Camille Gandiolle.

8 lessons of 1h30 and 14 tutorial and project sessions of 1h30 The knowledge will be tested by a MCQ (multiple-choice questionnaire) and the skills acquired will be tested by a project consisting in implementing a coupled system. The MCQ will represent 50% of the grad and a small part of the project will be evaluated individually.

- Strong - weak coupling;
- Coupling of different formulations;
- Coupling of different scales.
Then particular coupling, of interest for additive manufacturing will be studied in more details:
- Laser on powder: electro-thermal coupling
- Powder bed melt.

Continuum mechanics and one of the following courses: Materials, Transport phenomena, Thermodynamics.

None.

Février - Mars.

GIF-SUR-YVETTE