License 3

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The objective of this course is to give an introduction to numerical tools for solving partial differential equations from different fields of engineering. We will deal with the spectral method applied to the heat diffusion equation in a bar and the development of codes based on this technique. In particular, students will have to implement this method in Python in order to integrate the basics of this language and the versioning tools. The documents submitted by the students will be produced using the Latex word processor.  

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In a first part: to deepen the basic notions of differential calculus seen in L2.

In a second part: introduce the qualitative study of differential equations.

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The resistance of materials (RoM) is a particular discipline of the mechanics of continuous media allowing the calculation of stresses and strains in slender structures made of different materials (machines, mechanical engineering, building and civil engineering). It is a 1D static modeling of a deformable solid assimilated to a beam linked to a frame and subjected to external mechanical stresses.

The RoM allows the study of the global behavior of a structure (relationship between stresses - forces or moments - and displacements) to be reduced to that of the local behavior of the materials composing it(relationship between stresses and strains). Mechanical stresses can be seen as " cohesive forces " of the material. The deformations of a physical object are observed by a variation in its dimensions or in its overall shape.

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This first module of Fluid Mechanics aims to provide basic elements on the behavior of industrial fluids (air, water, hydraulic fluid) in order to dimension simple systems involving fluid in static or dynamic (flow rates, pressure, speed, pressure drops,...). Emphasis is placed on the study and design of hydraulic installations.

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Rheology is the study of the deformation and flow of matter under the effect of an applied mechanical stress. In the field of materials, this science concerns in particular the following fields

            - Viscoelasticity

            - Plasticity

            - Viscoplasticity

            - Non-Newtonian fluids

In practice, rheology allows the characterization of macroscopic mechanical properties of materials whose behavior escapes the classical theories of the elastic solid and Newtonian fluids (with constant viscosity). Such materials can thus be considered as having an intermediate behavior between the solid and the fluid, between the elastic and the viscous.

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This course aims at introducing the basics of physical hydrodynamics. The kinematic aspects are treated in a first step: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of the current and potential velocity functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, then the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This part will lead us to define the stress tensor and the Reynolds number to deduce the laminar or turbulent character of a flow. The course ends with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensor.

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The course links scientific computing and variational methods for mechanics and is designed to model simple physical equations and implement numerical methods to solve these equations.

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Acquire basic notions in numerical methods for differential equations

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TD language courses aimed at training the 5 language skills;

Oral comprehension & expression

Written comprehension & expression

Oral interaction

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• read a technical drawing of medium difficulty
• identify standard mechanical components on a drawing
• identify the operation of a mechanical system of moderate difficulty from an overall drawing
• draw a part in several views, following the rules of projection
• identify and draw cylinder-plane, cylinder-cylinder, plane-cone, cylinder-cone intersections
• draw cross-sections and sectional views
• extract a part from an overall drawing of moderate difficulty
• use of basic Solidwork functions (part mode, assembly and drawing)

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Research & Development (R&D) is both the product of teamwork and individual talents, all at the service of innovation (applied research) and knowledge (fundamental research). The themes are diverse and varied, but a certain methodology is necessary to approach any R&D problem.

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The objective of this course is the modeling of continuous solid media by restricting itself, for a first approach, to elastostatics under the assumption of small perturbations. We will find in this course the application of the fundamental principle of statics to deformable solids. The following concepts are introduced: tensors and tensor fields, algebra and tensor analysis, boundary problems, fundamental principle of statics, virtual power principle. Analytical techniques for solving classical problems and energetic approaches will be covered. This course is fundamental in the training of students in mechanics, both those who are oriented towards design and conception or towards R&D.

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Project entrusted to a group of two to three students, supervised by a tutor. Weekly meeting to follow up, help with the writing of a report and an oral presentation. The work is spread out over a semester and ends with the submission of a report and an oral presentation.

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This teaching unit is a first advanced module of mechanical design. It provides tools for the discriminating choice of technologies responding to the classical functions of mechanisms (embedding and rotational guidance by bearings), from a partially supplied functional specification, industrial documentation and regulatory standards. Practical work on the analysis of existing mechanisms and practical work on the design of basic technological solutions will complete this teaching.

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TD language courses aimed at training the 5 language skills;

Oral comprehension & expression

Written comprehension & expression

Oral interaction

Continuous speaking - presentations

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The resistance of materials (RoM) is a particular discipline of the mechanics of continuous media allowing the calculation of stresses and strains in slender structures made of different materials (machines, mechanical engineering, building and civil engineering). It is a 1D static modeling of a deformable solid assimilated to a beam linked to a frame and subjected to external mechanical stresses.

The RoM allows the study of the global behavior of a structure (relationship between stresses - forces or moments - and displacements) to be reduced to that of the local behavior of the materials composing it(relationship between stresses and strains). Mechanical stresses can be seen as " cohesive forces " of the material. The deformations of a physical object are observed by a variation in its dimensions or in its overall shape.

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This course introduces students to project management, taking into account the major issues of company performance. The student is put in a position to manage the key phases of the product design process.

This project-based teaching allows for the detailed analysis of each phase of the design process in the form of case studies. The student thus learns the methods for generating an idea (creativity, functional analysis) up to the generation of the product architecture.

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This first module of Fluid Mechanics aims to provide basic elements on the behavior of industrial fluids (air, water, hydraulic fluid) in order to dimension simple systems involving fluid in static or dynamic (flow rates, pressure, speed, pressure drops,...). Emphasis is placed on the study and design of hydraulic installations.

See full page

Rheology is the study of the deformation and flow of matter under the effect of an applied mechanical stress. In the field of materials, this science concerns in particular the following fields

            - Viscoelasticity

            - Plasticity

            - Viscoplasticity

            - Non-Newtonian fluids

In practice, rheology allows the characterization of macroscopic mechanical properties of materials whose behavior escapes the classical theories of the elastic solid and Newtonian fluids (with constant viscosity). Such materials can thus be considered as having an intermediate behavior between the solid and the fluid, between the elastic and the viscous.

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This course provides the basic tools necessary for the functional dimensioning of mechanical systems. After presentation of the one-dimensional dimensioning and its limits, the "3D" geometric tolerancing (GPS), according to the ISO standards, is introduced in order to learn how to read and write a geometric tolerance according to the functional needs of a part in a mechanical system. The study of the hyperstaticity of the mechanism and the connections allows then to set up the functional conditions required to ensure the assembly and the good functioning of the system. The determination of the dimensional and geometric tolerances is then carried out with the help of the implementation and the resolution of the chains of dimensions. Finally, once the parts have been produced, it is necessary to carry out metrological control and to check their conformity with the functional dimensioning.

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This UE is a central module of mechanical design technology. It allows to apply the concepts of dimensioning of standard components seen mainly in the UEs of technology in L2 (introduction to mechanical design) and L3 (structure and dimensioning, mechanical design 1 and 2) in the case of existing mechanical systems. It also indirectly calls upon all the other UEs of mechanics of the rigid and deformable solid seen mainly in L2 and L3.

Emphasis is placed on the discovery and comparison of real technological solutions, allowing to enrich the technological culture, and on the research, the critical choice and the pre-dimensioning of technological solutions compatible with the studied system starting from a specification of partial (re)design. Finally, the realization of the chosen solution is based on the sketch of a drawing in the sense of industrial design, both on paper and with the help of a CAD software with the complete dimensioning of one of the parts of the mechanism.

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This UE closes the teaching of technology of the Bachelor of Mechanics, course CDPI, composed of 4 modules. It aims at giving tools for understanding and dimensioning complex mechanical systems (automatic gearbox, power transmission mechanisms, ...).

This module is based for half of the teaching on courses / TD to study the pulley-belt systems, clutches / brakes and pre-stressed systems with applications on the mounting of preloaded bearings. In parallel, the teaching is based on practical work on the analysis of different mechanical systems (CVT gearbox, automatic gearbox, brake, clutch, preloaded bearing assembly, ... ), as well as on design practical work in order to implement the acquired skills on specific case studies.

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TD language courses aimed at training the 5 language skills;

Oral comprehension & expression

Written comprehension & expression

Oral interaction

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• read a technical drawing of medium difficulty
• identify standard mechanical components on a drawing
• identify the operation of a mechanical system of moderate difficulty from an overall drawing
• draw a part in several views, following the rules of projection
• identify and draw cylinder-plane, cylinder-cylinder, plane-cone, cylinder-cone intersections
• draw cross-sections and sectional views
• extract a part from an overall drawing of moderate difficulty
• use of basic Solidwork functions (part mode, assembly and drawing)

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Research & Development (R&D) is both the product of teamwork and individual talents, all at the service of innovation (applied research) and knowledge (fundamental research). The themes are diverse and varied, but a certain methodology is necessary to approach any R&D problem.

See full page

The objective of this course is the modeling of continuous solid media by restricting itself, for a first approach, to elastostatics under the assumption of small perturbations. We will find in this course the application of the fundamental principle of statics to deformable solids. The following concepts are introduced: tensors and tensor fields, algebra and tensor analysis, boundary problems, fundamental principle of statics, virtual power principle. Analytical techniques for solving classical problems and energetic approaches will be covered. This course is fundamental in the training of students in mechanics, both those who are oriented towards design and conception or towards R&D.

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This project is triggered by the request of a client (project owner) who comes to present his need to the students. It is an application that places the student in the position of a service provider to meet the client's need or request. This project aims to reproduce the methods used in business.

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