Applied Mechanics 1st year

The course explores fundamentals of kinematics of solid bodies; displacement and strain measures, to statics of solid bodies, stress tensor, equilibrium equations. The course is illustrated through various examples: traction-compression, torsion, bending, pressure vessels, truss. 

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The aim of this first part is to learn the principles of measurements of static and dynamic response of solid material and structures, and carry out the analysis of results: (i) Force and displacement measurements (type, performance and uses to perform standard experiments), (ii) full field measurement of displacement using 2D and 3D images (images acquisition, treatment and digital images correlation). All these techniques and methods are illustrated through experimental set ups available in research labs. 

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This first part of the course is dedicated on the theory and implementation of the finite element method for solving boundary value problems in solid mechanics: Overview of the finite element method in solid mechanics, the Finite Element Method for Static Linear Elasticity, The finite element method for time dependent and dynamic problems.

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This course gives a general overview of some of the most common techniques used in image and signal processing, with a special focus in Fluid Mechanics. It starts with a review of the basic concepts of both signals and image processing (systems, block diagrams, Fourier series, 1 and 2D Fourier Transforms, basic image manipulation, filters…). In a second stage, the course focalises in more complex statistical techniques like, for the case of signals, spectral analysis, correlation and structure functions. For the case of images, it covers the reconstruction of particle trajectories and the basics of PIV (Particle Image Velocimetry) analysis.  

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This course provides basics in fluid mechanics. This includes hydrostatic, fluid kinematics and Euler equation for ideal fluid. Bernoulli formula are then derived and examples of application are presented. The case of non-ideal fluid and Navier-Stokes formula are afterwards established. The NS equation is solved for classical simple cases (e.g. Couette flow). Turbulence is shortly introduced during a 3h practical course held at the Coriolys experiment.

This course comprises 21h of CM/TD, and a 3h practical course.

The final exam is a 2h examination. The "controle continu" is a written homework.

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The course aims to provide the students with the basic concepts of mechanics of materials: classification of the different mechanical behaviours, elasticity and criteria formulations, plasticity, visco-plasticity.

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An overview of discrete element simulations, force transmission in granular packings,  another vision of soil mechanics, microscopic origins of some constitutive laws, role of the geometry,  numerical homogenization,  "Tools" for characterizing the microstructure, complex systems and strong coupling. 

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Multiphysics models deal with multiple simultaneous physical phenomena, which include, but are not limited to, coupling between solid and fluid mechanics, heat and mass transfer. Knowledge obtained through these models can be applied in many industrial fields and help us in the decision making process.

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Fundamental equations, dimensionless numbers. Forced convection in laminar boundary layers. Internal laminar flows. External and internal natural convection. Turbulent convection in internal and external wall flows. Turbulent convection in free shear flows. 

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This course presents basic notions on instabilities and turbulence. We try to be as progressive as possible and to base our presentation on analyses of real experiments and real flows. We review few mathematical methods to analyze nonlinear systems in terms of instabilities. The students have to use their new knowledge to run and analyze numerical simulations of very simple systems. We then study some of the most important physical mechanisms for fluid instabilities and the corresponding criteria. We quickly present a zoology of common fluid instabilities and discuss the mechanisms and the possible technical implications. We give a broad introduction on turbulence and describe few fundamental methods and results, in particular the Richardson cascade, the Reynolds decomposition and the Kolmogorov spectra.

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The course aims to provide the students with the basic concepts of geomechanics, that is the theoretical and applied science dealing with the mechanical behavior of geomaterials (soil and rock). The first part of the course covers the basic subjects of geomechanics such as stress and strain, permeability and consolidation, compressibility, shear strength, testing techniques, etc. The course then focuses on the mechanical behaviour of geomaterials and provides a basic understanding of the features that are specific to geomaterials (dilatancy, friction, pressure dependence) and the modelling of such complex phenomena. In particular, an introduction is given to the ideas and concepts of elastoplasticity, this subject being of critical importance to geomechanics and geotechnical engineering. 

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This course aims at providing the basic knowledge on waves propagation in fluid and in solid medium. Governing equations for various situations will be considered and solutions will be derived. The analysis will cover the field of vibrations in solid media (1D string vibration, 2D plate vibrations,...), acoustic waves in air, gravity and inertia waves in the atmosphere and the ocean.   Dispersion and attenuation processes will be considered as well and will be related to physical aspects (wave in a duct, thermodynamic properties of the medium, compressibility effects, etc...)

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Environmental flows lecture aims at introducing geophysical fluid dynamic and showing how mechanistic approaches are commonly applied to describe the flows. The atmospheric boundary layer (ABL) is presented as an example, It is associated with its boundary conditions, namely the energy budget at the surface and the geostrophic circulation at the top.

1. Introduction and surface boundary conditions for ABL
2. Mathematical decription of ABL
3. Introduction to turbulence
4. Similarity theory
5. Measurements in ABL

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This course aims at introducing the basic knowledge on the dynamics of geophysical fluids, which are fluids influenced by the rotation of the Earth and by the fact that their density varies along the vertical. Examples are the ocean and the atmosphere. The main balances to which these fluids obey wil be presented along with several classical models, such as the shallow-water-model. Applications to the ocean and the atmosphere will be illustrated by observations, laboratory experiments and numerical modellling. 

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The modelling of mechanical properties of materials and structures is a complex subject. In some applications, it is sufficient to assume that the material remains elastic. However, such a simplified assumption is appropriate only within a limited range, and in general must be replaced by a more realistic approach that considers the inelastic processes such as plastic yielding. The course aims to provide the students with the basic concepts of plastic analysis of structures: limit analysis, multiaxial stress-strain relations, limit state theorems, concept of plastic hinges and yield line of plates, calculation of collapse load and displacement at incipient collapse, application to engineering materials.

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The aim of the course is to give the students an opportunity to perform a research project in a lab within the field of solid or/and fluid mechanics solid under supervision according to an individual study plan, to summarize the results in a research report and present the results of the project. 

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The aim of this second part is to learn the principles of measurements in fluid mechanics, and carry out the analysis of results: Flow Measurements Techniques – Integral flow properties (rotameter…) and local flow properties (Hot Wire Anemometer, Laser Doppler Anemometer, Particle Image Velocimetry, Ultrasonic Technique, Magnetic Technique… ). All these techniques and methods are illustrated through experimental set ups available in research labs. 

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This second part of the course introduces students to finite difference methods as a means of solving different type of differential equations that arise in fluid dynamics.
Fundamentals of numerical analysis, ordinary differential equations and partial differential equations related to fluid mechanics and heat transfer will be reviewed.
Error control and stability considerations are discussed and demonstrated.
A simple code using the finite difference method will be developed, tested and used on a one-dimensional partial differential equations.

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The course aims to provide the students with the basic concepts of mechanics of materials: classification of the different mechanical behaviours, elasticity and criteria formulations, plasticity, visco-plasticity.

Visit the full page about this course

An overview of discrete element simulations, force transmission in granular packings,  another vision of soil mechanics, microscopic origins of some constitutive laws, role of the geometry,  numerical homogenization,  "Tools" for characterizing the microstructure, complex systems and strong coupling. 

Visit the full page about this course

Multiphysics models deal with multiple simultaneous physical phenomena, which include, but are not limited to, coupling between solid and fluid mechanics, heat and mass transfer. Knowledge obtained through these models can be applied in many industrial fields and help us in the decision making process.

Visit the full page about this course

Fundamental equations, dimensionless numbers. Forced convection in laminar boundary layers. Internal laminar flows. External and internal natural convection. Turbulent convection in internal and external wall flows. Turbulent convection in free shear flows. 

Visit the full page about this course

This course presents basic notions on instabilities and turbulence. We try to be as progressive as possible and to base our presentation on analyses of real experiments and real flows. We review few mathematical methods to analyze nonlinear systems in terms of instabilities. The students have to use their new knowledge to run and analyze numerical simulations of very simple systems. We then study some of the most important physical mechanisms for fluid instabilities and the corresponding criteria. We quickly present a zoology of common fluid instabilities and discuss the mechanisms and the possible technical implications. We give a broad introduction on turbulence and describe few fundamental methods and results, in particular the Richardson cascade, the Reynolds decomposition and the Kolmogorov spectra.

Visit the full page about this course

The course aims to provide the students with the basic concepts of geomechanics, that is the theoretical and applied science dealing with the mechanical behavior of geomaterials (soil and rock). The first part of the course covers the basic subjects of geomechanics such as stress and strain, permeability and consolidation, compressibility, shear strength, testing techniques, etc. The course then focuses on the mechanical behaviour of geomaterials and provides a basic understanding of the features that are specific to geomaterials (dilatancy, friction, pressure dependence) and the modelling of such complex phenomena. In particular, an introduction is given to the ideas and concepts of elastoplasticity, this subject being of critical importance to geomechanics and geotechnical engineering. 

Visit the full page about this course

This course aims at providing the basic knowledge on waves propagation in fluid and in solid medium. Governing equations for various situations will be considered and solutions will be derived. The analysis will cover the field of vibrations in solid media (1D string vibration, 2D plate vibrations,...), acoustic waves in air, gravity and inertia waves in the atmosphere and the ocean.   Dispersion and attenuation processes will be considered as well and will be related to physical aspects (wave in a duct, thermodynamic properties of the medium, compressibility effects, etc...)

Visit the full page about this course

Environmental flows lecture aims at introducing geophysical fluid dynamic and showing how mechanistic approaches are commonly applied to describe the flows. The atmospheric boundary layer (ABL) is presented as an example, It is associated with its boundary conditions, namely the energy budget at the surface and the geostrophic circulation at the top.

1. Introduction and surface boundary conditions for ABL
2. Mathematical decription of ABL
3. Introduction to turbulence
4. Similarity theory
5. Measurements in ABL

Visit the full page about this course

This course aims at introducing the basic knowledge on the dynamics of geophysical fluids, which are fluids influenced by the rotation of the Earth and by the fact that their density varies along the vertical. Examples are the ocean and the atmosphere. The main balances to which these fluids obey wil be presented along with several classical models, such as the shallow-water-model. Applications to the ocean and the atmosphere will be illustrated by observations, laboratory experiments and numerical modellling. 

Visit the full page about this course

The modelling of mechanical properties of materials and structures is a complex subject. In some applications, it is sufficient to assume that the material remains elastic. However, such a simplified assumption is appropriate only within a limited range, and in general must be replaced by a more realistic approach that considers the inelastic processes such as plastic yielding. The course aims to provide the students with the basic concepts of plastic analysis of structures: limit analysis, multiaxial stress-strain relations, limit state theorems, concept of plastic hinges and yield line of plates, calculation of collapse load and displacement at incipient collapse, application to engineering materials.

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

Visit the full page about this course

The aim of the course is to give the students an opportunity to perform a research project in a lab within the field of solid or/and fluid mechanics solid under supervision according to an individual study plan, to summarize the results in a research report and present the results of the project. 

Visit the full page about this course