L3 - CUPGE Mechanics

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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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