L3 - CUPGE Mechanical Engineering

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The objective of this course is to provide an introduction to numerical tools for solving partial differential equations arising in various fields of engineering. We will cover 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 be required to implement this method in Python in order to learn the basics of this language and versioning tools. Students' work will be produced using the Latex word processor.  

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The emphasis is on the performance and limitations of engineering calculation methods so that students are able to use them correctly "in real-life situations." This real-life application is certainly the most challenging aspect of this introduction to scientific calculation, as it requires not only a certain physical understanding, but also a step back from mathematical modeling and a minimum level of computer skills.

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In the first part: deepen the basic concepts of differential calculus covered in L2.

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

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Material resistance (RdM) is a specific discipline of continuum mechanics that enables the calculation of stresses and deformations in slender structures made of different materials (machinery, mechanical engineering, building, and civil engineering). It involves 1D static modeling of a deformable solid assimilated to a beam connected to a frame and subjected to external mechanical stresses.

RdM allows the study of the overall 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 the " cohesive forces " of the material. The deformations of a physical object can be observed as a change in its dimensions or overall shape.

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This first module in fluid mechanics aims to provide basic information on the behavior of industrial fluids (air, water, hydraulic fluid) with a view to designing simple systems involving fluids in static or dynamic conditions (flow rates, pressure, speed, pressure drops, etc.). The focus is 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 applied mechanical stress. In the field of materials, this science is particularly relevant to the following areas:

            - Viscoelasticity

            - Plasticity

            - Viscoplasticity

            - Non-Newtonian fluids

In practice, rheology is used to characterize the macroscopic mechanical properties of materials whose behavior defies classical theories of elastic solids and Newtonian fluids (with constant viscosity). Such materials can therefore be considered as having behavior that lies between that of solids and fluids, between elastic and viscous.

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This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential 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 ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, 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 knowledge of numerical methods for differential equations

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Language tutorial courses aimed at training the five language skills;

Listening comprehension & speaking

Reading comprehension & writing

Oral interaction

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• read a technical plan of medium difficulty
• recognize standard mechanical components on a drawing
• identify how a moderately difficult mechanical system works based on an overall plan
• draw a part in multiple views following the rules of projection
• Identify and draw the intersections of cylinder-plane, cylinder-cylinder, plane-cone, and cylinder-cone.
• draw cross-sectional views and sections
• extract a part from a medium-difficulty assembly drawing
• use of the basic functions of Solidworks software (parts mode, assembly, and drafting)

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Research and Development (R&D) is both the combination of a team's work and individual talents, all in the service of innovation (applied research) and knowledge (fundamental research). The topics are diverse and varied, but a certain methodology is necessary to address any R&D issue.

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The objective of this course is to model continuous solid media, initially focusing on elastostatics under the assumption of small perturbations. In this course, we will explore the application of the fundamental principle of statics to deformable solids. The following concepts are introduced for this purpose: tensors and tensor fields, tensor algebra and analysis, boundary value problems, the fundamental principle of statics, and the principle of virtual work. Techniques for the analytical solution of classical problems and energy approaches will be discussed. This course is fundamental to the training of students in mechanics, whether they are oriented towards design and engineering or towards R&D.

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Project assigned to a group of two to three students, supervised by a tutor. Weekly meetings to monitor progress and provide assistance with writing a report and preparing an oral presentation. The work is spread over one semester and concludes with the submission of a report and an oral defense.

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