Mechanical engineering
Design | Dimensioning | Prototyping Modeling | Simulation | Energy and Sustainable Development | Transport, Energy, Sport
The department trains multi-skilled mechanical engineers capable of leading or participating in projects based on the design, optimisation and realisation of innovative products, facilities and procedures. Training in this area combines mastery of scientific and technological knowledge with learning about state of the art digital simulation tools. The aim is to cultivate the future engineers creativity and encourage them to resolve concrete problems, while taking into account the individual and his/her environment, within a project team.
The program offered combines scientific and technological teaching, with cross-disciplinary and soft skills modules (languages, economics, marketing, general management and project management) and practical experience acquired through projects and work placements (in industry, R&D departments, research laboratories…)
Concerning the scientific and technical aspects of the program, a strong emphasis is placed on understanding physical phenomena, as well as their modelling and numerical simulation.
An area which is also dealt with is the interaction with related sciences, such as mechatronics, materials of the future, acoustics, etc.
Regarding project management, this area is integrated in the projects carried out in both 3rd and 4th years. These projects, which are based on both innovation and design, can be carried out individually or within a group.
Students are offered a number of different modules and outlets in order to allow them to construct their own career plan. The final year is mainly devoted to modules within the chosen specialisation or more research-oriented taught modules for those who wish to continue their studies with a PhD. It is also possible to undertake the final year of studies abroad.
The department encourages community and clubs within the school via initiatives such as the « 4L Trophy » (humanitarian rally), the « trophée SIA » (development of innovative vehicles), the realisation of hybrid / electronic vehicles and the development of renewable energy systems.
Classes are taught in French.
Activity sectors
- Aeronautical, sea and automobile transport
- Energy
- Research
- Design offices
- Chemical and medical industries
Links with research units
Associated research unit :
- UML - Fluid mechanics and mechanics of materials and Structures
- LaMcube - Multiscale and Multiphysics Mechanics
Program
UE5-1 Mathematics and Computing I
- Prerequisites :
Mathematics up to second-year scientific university level. Additional personal work may be required for certain training courses (in particular BTEC).
- Goals to be achieved :
- Being able to solve differential systems and differential equations of order greater than or equal to 1.
- Being able to calculate Fourier series or Fourier transforms and use them to calculate sums of series, generalized integrals, or solve differential equations. Application to the heat equation. - Course details :
Part I - Scalar and System of Differential Equations - Lectures=9h - Tutorials=14h
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Chapter 1 - First order differential equations
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- Equations with separable variables - Homothetic equations - Generalization to equations of the type y' = rational fraction of linear forms
- Linear differential equations of the 1st order - Vector space of solutions of the equation without second member - Affine space of solutions of the equation with second member (linear superposition) - Lagrange method (or "variation of the constant") to calculate the particular solution - Uniqueness of the particular solution
- Examples of nonlinear equations: Bernoulli equation, Lagrange equation
Chapter 2 - Second Order Linear Differential Equations
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- Linearly dependent and independent solutions - Wronskian - Vector space of solutions of the equation without a second member - Analytical solution knowing a particular solution
- Affine space of solutions of the equation with second member (linear superposition) - Lagrange method (or "variation of constants") to calculate the particular solution
- Special case of the equation with constant coefficients: Characteristic equation - The 3 solution families (harmonic oscillator, damped harmonic oscillator, degenerate case).
Chapter 3 - Linear Differential Systems of Order 1
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- Interpretation of the 2nd order scalar equation as a Vector Differential System of order 1 with 2 equations - Vector spaces and affine solutions of the system without and with second member - Lagrange method revisited
- Generalization to the scalar equation of any order n = Vector Differential System of order 1 with n equations
- Generalization to the Differential System with any matrix A - Wronskian differential equation with separable variables (W'=tr(A). W)
- Special case where the matrix A is constant - Resolution method by reduction of the matrix A (diagonalizable or trigonalizable. Resolution method by derivation.
Part II - Series and Fourier Transform - Lecture=5h - TD=10h
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Chapter 1 - Fourier series
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- Trigonometric series - Sufficient convergence condition - Calculation of real coefficients in (cos,sin)
- Development of a periodic function in Fourier series (DSF) - Dirichlet's theorem
- Properties of Fourier coefficients: Parity/imparity of the function, Frequency delay, Complex expression of Fourier coefs - Power spectrum - Bessel-Parseval formula (conservation of energy) - Application to the calculation of Riemann series. - Solution of the heat equation in a bar of thin section.
Chapter 2 - Fourier Transform
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- Fourier-Plancherel integral of a summable function (L1) - Physical interpretation of the wave number
- Properties of the Fourier Transform: Absolute convergence, Linearity, Continuity, Conservation of parity, Homothety, Derivation, Translation, Frequency delay, Fourier transform of the derivative of a function (Application to differential equations)
- Inverse Fourier transform - Analogy with Dirichlet's theorem
- Convolution product
- Power spectrum - Plancherel-Parseval formula (conservation of energy) - Reading list :
Ressources infinies en ligne
20 h Tutorial
3 h DS
- Prerequisites :
Mathématiques générales
- Goals to be achieved :
- Know what is scientific programming
- Be fluent in the usage of a programming language (Python)
- Be able to translate into code simple algorithms , to manipulate data and to represents them graphically - Course details :
This is an introductory course in scientific programming and the Python language. The course is structured around a theoretical introduction (2 CM sessions) and 3 learning practical sessions and a knowledge control practical session.
The course support was created in Jupyter Notebook. The application of computer science concepts is done through the creation of programs (scripts) which deal with simple problems in the field of mechanics.
Lectures :
- Introduction to scientific programming (floating point numbers, rounding errors)
- Introduction to computer languages
- Python language basics (variables, lists, conditionals, loops, functions, modules, vectors, matrices, numpy and matplotlib libraries)
TP1:
– Introduction to Linux commands
– Script 1: enter or display text and data
– Script 2: perform simple operations on variables
– Script 3: read data from a file and set it [pression.txt]
– Script 4: graphical representation of data
TP 2:
– Use functions in Python
– Create and manipulate a multidimensional array with the numpy library
– Graph a matrix
– Script 1: enter or display text and data
– Script 2: study of the transfer function of the spring – shock absorber (suspension) system of an automobile
– Script 3: Calculation of the critical value of the quality coefficient of a suspension
– Script 4: preparation-of-input-data-for-a-numerically-controlled-machine-tool
TP 3
– Script 1: understand shear type deformation
– Script 2: transport of the velocity vector
– Script 3: propagation of a disturbance
– Script 4 (bonus): Moments of inertia of an aluminum plate
TP 4
– Knowledge control practical work
TP 5
- Exercises on the usage os spreadsheets
20 h Practical
UE 5-2 Mechanics I
UE5-3 Design and Manufacturing I
UE5-4 Soft Skills I
Unit 5-5 Languages
UE 6-1 Mathematics and Computing II
- Prerequisites :
511110
- Goals to be achieved :
- Know the Laplace transform and its main applications, in particular the resolution of equations and systems of differential equations, and integro-differential equations, and the calculation of certain improper integrals;
- Know how to calculate a double integral and a triple integral. Application to the calculation of planar areas, warped surface areas, volumes, center of gravity and moments of inertia.
- Course details :
Part I - Laplace Transform - Lectures=4h, Tutorials=6h
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Chapter 1 - Laplace integral
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- Laplace integral of a causal function - Sufficient conditions of existence - Convergence abscissa - Limit to infinity of a Laplace transform
- Laplace transforms of some usual functions (unit scale, exponential, integer power function, etc.)
Chapter 2 - Properties of the Laplace Transform
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- Linearity - Application to hyperbolic and circular functions
- Laplace transform of the derivative of a function - Generalization to the derivative of any order
- Laplace transform of x^n.f(x)
- Homothety
- Delay formula - Application to the Laplace transform of a periodic function
- Frequency delay formula
- Laplace transform of the primitive of a function
- Integration of the Laplace Transform or "rule of division by x" - Application to cardinal sine
- Initial value theorem
- Final value theorem - Application to the calculation of the Dirichlet integral
Chapter 3 - Inverse Laplace Transform
---------
- Bronwich-Mellin formula
- Practical calculations of inverse transforms - Inverse use of properties - Reduction into simple elements
Chapter 4 – Convolution Product
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- Borel's theorem
- Applications: resolution of integro-differential equations, calculation of the inverse transform of a product
Chapter 5 - Resolution of linear differential equations and systems by Laplace Transform
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- Equivalent algebraic equation(s) in Laplace space - Calculation of the solution by inverse transform
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Part II - Multiple Integrals - Lectures=4h, Tutorials=4h
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Chapter 1 - Double Integrals
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- Pavable part of R^2 - Quadrable part of R^2
- Double integral of a bounded function of R^2 in R: Darboux sums, Riemann sums - Fundamental theorem
- Geometric interpretation of the Double Integral = Volume of a rectilinear cylinder
- Properties: Linearity, Chasles relation, Monotonicity, Upper boundedness, Average formula
- Analytical calculation of a double integral: Simply connected domain of R^2 - Fubini formula
- Change of variables - Diffeomorphic Jacobian - Example: polar coordinates, calculation of the Gauss integral
Chapter 2 - Triple Integrals
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- Pavable part of R^3 - Cubable part of R^3
- Triple integral of a bounded function of R^3 in R
- Analytical calculation of a triple integral: Simply connected domain of R^3 - Fubini formula
- Change of variables - Examples: spherical and geocentric coordinates, cylindrical-polar coordinates
Chapter 3 - Applications of Multiple Integrals
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- Calculation of planar areas
- Calculation of warped surface areas
- Calculation of volumes
- Moments of inertia and Center of gravity - Reading list :
Ressources infinies en ligne
12 h Tutorial
3 h DS
- Prerequisites :
511120|511110
- Goals to be achieved :
Knowing and being able to use numerical methods to solve engineering problems.
Being able to tune parameters to improve convergence and accuracy of results.
* in lectures and exercise classes :
- Providing the basic techniques for solving the main basic problems in numerical analysis.
- Exposing the student to the use of numerical methods to solve engineering problems.
* Practical work:
- Introducing students to the specific problems related to the informatical implementation of numerical methods.
- Knowing how to use informatic tools to solve mechanical engineering problems.
* Expected skills at the end of the module:
- Knowing and being able to use numerical methods to solve "classical" problems.
- Knowing how to apply (program) numerical-method algorithms to solve engineering problems.
- Understanding numerical techniques and being able to parameterize them to improve convergence and accuracy of results. - Course details :
in lectures and exercise classes:
1. numerical solution of non-linear algebraic equations
2. numerical solution of ordinary differential equations
3. numerical solution of algebraic linear systems
4. numerical calculation of eigenvectors and eigenvalues
in practical work:
Programming with Python language:
1. Solving a non-linear algebraic equation for an application: equilibrium of a mechanical system - a sphere in a basin filled with steady fluid
2. Numerical resolution of ordinary differential equations: computation of trajectories of moving objects in air
3. Solving linear systems: least-squares methods and analysis of experimental data
4. Evaluation
8 h Tutorial
16 h Practical
1 h DS
- Goals to be achieved :
-•Be aware of:
- risks (personal/confidentiality/economic/societal)
- the possibilities/limitations of digital tools
- your own cognitive biases.
•Understand the nature of data and its impact.
•Know, understand, and apply the university's charter on ISAGs.
•Have the necessary knowledge to understand how computers/algorithms/artificial intelligence work.
•Choose your digital tools in a reasoned manner and be able to justify your choice
- Course details :
Summary program defined by each specialty - Reading list :
UE 6-2 Mechanics II
UE 6-3 Design and Manufacturing II
UE 6-4 Project and Soft Skills II
Unit 6-5 Languages
UE -7-1 Vibration - Transfer
- Prerequisites :
511240
- Course details :
- Study of continuous media (transition from discrete to continuous, typical problems, general formulation, use of differential operators, modal analysis and discretization techniques). 4h course - 4h tutorial
- Forced vibration responses of continuous systems (resonance phenomenon). 4h course - 4h tutorial
- Approximate methods (Concentrated masses, Rayleigh, Rayleigh-Ritz, Dunkerley, Finite Elements). 4h course - 4h tutorial
-Experimental methods and notions of damping. Course 2h - Tutorial 2h
- Application through a series of Practical Work. 12h practical work and an 8h project related to the Finite Element Computation - Reading list :
Théorie des vibrations, M. Géradin, D. Rixen, Editions MASSON
16 h Tutorial
12 h Practical
8 h Project
1 h DS
- Prerequisites :
512110
- Goals to be achieved :
- Acquire and apply knowledge and methods for solving problems involving heat transfer: mechanisms and physical laws of conduction, convection and radiation; methods for solving stationary and transient problems; energetic optimisation. - Course details :
- Heat transfer: heat generation (combustion, joule effect, friction, etc.); modes of heat transfer and associated laws (conduction, convection, radiation); methods of solving steady-state problems (heat flow balance, thermal resistances, etc.); notions of methods of solving transient problems; solving problems requiring modelling, identifying relevant hypothesis (orders of magnitude, ranking of phenomena involved, etc.); introduction to methods of measuring flow and temperature (thermocouples, infrared camera, etc.). - Reading list :
Manuel de thermique EYGLUNENT Hermes
Initiations aux transferts thermiques SACADURA Technique Et Documentation
Heat transfer HOLMAN Mac Graw Hill Editions
Conduction of heat in solids CARSLAW & JAEGER Oxford University Press
22 h Tutorial
12 h Practical
6 h Project
3 h DS
UE -7-2 Numerical Methods I
UE 7.3 Design I
UE 7-4 Soft Skills I
Unit 7-5 Languages
UE-8.1 Numerical Methods and Sizing
- Prerequisites :
512210|513210
- Goals to be achieved :
Understand and identify the different types of fatigue, particularly that of unlimited endurance (high cycle fatigue).
Be able to check the resistance of a structure for high cycle fatigue (polycrystals).
- Course details :
The concept of cyclic loading and the physical mechanisms of fatigue failure
Conventional tests and plots (Wohler)
Endurance limit and experimental determination methods - Dispersions: origin and normal law
Fatigue strength verification under cyclic uniaxial loading without and with mean loading (Haigh)
Damage accumulation
Fatigue strength verification under multiaxial loading (critical plane type criteria): analytical and numerical calculations
Application to practical industrial configurations (intervention by professionals) - Reading list :
Fatigue des matériaux et des structures : Tome 1, Introduction, endurance, amorçage et propagation des fissures, fatigue oligocyclique et gigacyclique. C. Bathias et A. Pineau.
Essais mécaniques et lois de comportement. D. François
Fatigue des structures : Endurance, critères de dimensionnement, propagation des fissures, rupture. G. Henaff et F. Morel
12 h Tutorial
8 h Practical
1 h DS
- Prerequisites :
513210
- Goals to be achieved :
- Modelling a mechanical system for its design (definition of the type of geometric model, choosing the type of finite element and computational assumptions, operating results of static analysis, dynamic and thermal)
- Write a report about the sizing.
- Have a critical look at the results achieved by software
- Course details :
Practical work (20h): - Examples issued from mechanical systems industrially allowing the implementation of a sizing method: - Introduction to the sizing of complex connections (contact connections, prestressed connections, etc.), - Introduction to topology optimization
UE8-2 Design II
UE8-4 Assistant Engineer Placement : starting in May (10-13 weeks)
UE8-4 Soft Skills II
UE 8-5 Languages
UE9-1-Specialty Modules
- Prerequisites :
512220|513230|511110|512120
- Goals to be achieved :
Acquiring basic knowledge of real (viscous) fluid mechanics. Understanding the interest of industrial modeling, concrete examples. Methodology for problem solving in aerodynamics and hydrodynamics of viscous flows. Computing forces (drag, lift) on obstacles in flows of practical interest. Introduction to turbulence and its modeling. - Course details :
Course and exercice classes:
- Real fluids and forces on obstacles
- Dimensional analysis and similarity
- Boundary layer
- Turbulence: main characteristics
- Turbulence and mean flow (RANS)
- Statistical approach to turbulence
- Turbulence modeling.
Practical work: Modeling with Ansys/Fluent
1. Laminar and turbulent pipe flows.
Laminar vs. turbulent Poiseuille velocity profiles. Skin friction coefficient. Comparison with Blasius correlation. 2-equation turbulence model of k-epsilon type, with or without wall functions.
2. Flow in an exhaust system.
Boundary layer thickness (Blasius formula). Boundary layer meshing, friction velocity, size of first cell. Eddy visualisation, recirculation zones.
3. Fuel filter.
Flow in a porous media. Head loss and head loss coefficient.
4. Wind turbine.
Power coefficient of a wind turbine. Mesh quality in a complex geometry (angular skewness criterion). Advanced visualisation with CFDPost : Pressure contours on the intrados and extrados of the blades ;Wake of the wind turbine.
5. Flow around a car body.
Setup of a numerical wind tunnel. Cx and Scx computation. Negative lift computation (ground effect). Advanced visualisation with CFDPost : Pressure contours on the car body ; Streamlines (detachment at the trailing edges) ; Wake of the car.
6. Free surface flow.
Unsteady air-water flow in a rotating bowl. VOF (Volume Of Fluid) method for free surface tracking. Advanced visualisation with CFDPost : creation of an animation movie.
- Reading list :
- Goals to be achieved :
Material and geometric non-linearities are addressed here, focusing on two major classes of behaviour: plasticity and hyperelasticity, and on contact problems. The aim is to raise the awareness of students who, in their future careers, may be required to dimension structures presenting such difficulties. - Course details :
Part 1: Plasticity
Isotropic and anistropic plasticity criteria: Von Mises, Tresca, Hill, etc.
formulation of constitutive laws in plasticity: load surface, normality rule, plastic multiplier,
examples of isotropic and kinematic strain-hardening behaviour laws
Part 2: Hyperelasticity
general information on polymers and elastomers
deformation energy density in hyperelasticity
some examples of Strain energy density functions: Generalised Rivlin, Ogden, Arruda-Boyce...
Part 3: Applications and projects
Practical problems and finite element projects are used to illustrate the course. Firstly, the various non-linear problems are explored. The practical work then focuses on the direct application of the course, with the emphasis on numerical convegence (Newton-Raphson method, radial return method, etc.). Finally, projects (stenting an artery, etc.) are proposed.
- Reading list :
8 h Practical
14 h Project
- Prerequisites :
511320|512320
- Goals to be achieved :
Model and/or reconstruct from a 3D scan a part in surface modeling under 3D Experience
Choose a potentially innovative material/geometry/process triptych on a particular point
Criticize and document the solutions chosen after implementation - Course details :
The leraning is organized around a project.
Contributions of courses and mini TP of use of 3D experience can be set up at the request of students.
Project Flow:
Surface modeling/ 3D scan/ reconstruction
Bibliographic study of the envisaged processes and materials (resin, composite, ...)
Design of "mold" in the broad sense allowing the obtaining of a part in very small series
Realization of molds in machining and/ or 3D printing
Creation of one or more pieces
Critical analysis of results and solutions
Documentation
28 h Project
- Prerequisites :
511330|512210|513120|513210|514120|514110
- Goals to be achieved :
Identify the mechanisms associated with tribology (dry frictional contacts) for friction, wear and friction-induced phenomena (vibrations, noise, particle emissions, etc.).
Design a braking system combining different multi-physics aspects: tribology; thermomechanics; vibrations.
- Course details :
This module is divided into different parts in such a way as to provide a complete overview of the problems associated with the design of a braking system, treated as an example of tribology applied to dry friction.
The concepts of tribology, thermomechanical couplings, materials and friction-induced vibrations are initially dealt with separately.
A common thread is used, dealing with the design of a railway brake system, to apply the concepts covered.
Tests on braking benches are used to understand the definition of representative tests, multi-physics instrumentation and data processing.
Thermomechanical aspects are modelled using the finite element method. The aim is to design a friction braking system with a view to achieving a certain number of performance targets. The modelling of a 'digital contact' is also covered at this stage.
Finally, each year a practical application is proposed, linked to an industrial problem posed by a partner (ALSTOM, HITACHI, etc.).
- Reading list :
- Reading list :
- Choix des matériaux en conception mécanique, Livre de Michael Ashby, 1992, Edition DUNOD
- Sélection des matériaux métalliques, P. CHOMEL, Techniques de l’Ingénieur.
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24 h Project
- Goals to be achieved :
At the end of this course, the future engineer must be able to:
- use a method of analyzing a flow around an aerodynamic profile
- explain how an aircraft flies (in subsonic flight).
- explain the balance of an aircraft in longitudinal flight.
- estimate, using a simplified analytical approach, the aerodynamic actions on a profile, a wing, an aircraft.
- analyze the performance of an aircraft based on its design characteristics: morphology, propeller, control surfaces and flight controls, etc.
- participate in the design of an aircraft by collaborating with specialists in the aeronautical field. - Course details :
Theory of potential flows,
Thin profile theory.
Calculations of aerodynamic forces on a 2D profile, a 3D wing.
Equilibrium and stability of longitudinal (subsonic) flight
Flight controls and trim
Thrusters
Electric planes
Helicopters: history of the different design and technical developments. - Reading list :
Pierre Lecomte - Mécanique du vol : les qualité de vol de avions et des engins - Éd. DUNOD, Dépot légal n° 3.926 décembre 1961 - Paris - 1962.
Boulet, Jean - L'Histoire de l'hélicoptère racontée par ses pionniers - Paris - Éd. France-Empire -1982
Manuel du pilote d'avion, formation initiale et maintien de compétence - Éd. Cépduès - ISBN : 9782364939011 - 2022 (19ième édition).
Jean Zilio - Guide pratique du pilotage - Éd. Cépduès - ISBN : 9782364939462 - 2023 (20ième édition).
28 h Project
- Prerequisites :
511110|512110|512120|511210|512210|513210|514120
- Goals to be achieved :
At the end of this course, the student will be able to:
• Understand the fundamental concepts of artificial intelligence (AI) and deep learning.
• Introduce the main AI and machine learning algorithms in a mechanical engineering context.
• Distinguish between different deep learning architectures (convolutional neural networks) and their specific applications.
• Integrate AI and deep learning techniques into simulation and optimization systems to solve complex mechanical engineering problems. - Course details :
• Introduction to Artificial Intelligence (AI): basic concepts, history and evolution of AI, distinction between symbolic AI and data-driven AI.
• Machine Learning: types of learning (supervised, unsupervised, reinforcement), introduction to regression, classification, and clustering models.
• Introduction to Deep Learning: definition and fundamental concepts of neural networks.
• Artificial Neural Networks (ANN): structure of a neuron, multilayer perceptrons (MLP), activation functions, backpropagation, and optimization.
• Convolutional Neural Networks (CNN): applications to images and grid-structured data (examples: image analysis, pattern recognition in mechanics).
• Practical implementation with modern tools: use of Python libraries (TensorFlow, Keras) for implementing AI models.
• Practical case studies: solving industrial problems using AI tools (examples of real cases, material fatigue analysis, prediction of deformation under load).
1 h DS
