M1 - Calculations and Simulations in Mechanical Engineering

The aim of this course is to introduce students to the finite element method as applied to one-, two- and three-dimensional problems in engineering and applied science. This presentation is made within the framework of linear elasticity and small perturbations in statics. Starting with prerequisites in mathematics and solid mechanics, the principle of discretization is first addressed through the approaches of Ritz and Gallerkine for one-dimensional media. Next, the problem of numerical integration is approached using the Gauss method. Meshing and validation of computational models is then addressed in the study of surface modeling with 2D elements. Finally, these notions will be used to set up the complete formalism of the finite element method within the framework of bar and beam elements, then triangle-type elements. A practical application of these important theoretical notions is carried out on an industrial calculation code (ANSYS) during practical work and a project.

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This course aims to prepare students for professional interviews by giving them the keys to value their past experiences.

This teaching is based on interview simulation games constructed on the basis of existing job offers.

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This unit introduces students to:

- management in the company, by presenting the company as an economic and legal entity on the one hand and by approaching the strategic approach in its entirety on the other.

- marketing in the company, from market research to operational marketing. The marketing approach will be directly applied to the industrial creation project carried out by the student teams.

The course sessions will be complemented by a company visit, as well as by the methodological approach of concretecase studies.

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This 42h course is divided in two parts (1/3, 2/3) in order to give the basic elements in heat transfer and fluid mechanics (3D). Fluids will be considered as continuous media. We will call a particle an element of infinitely small volume for a mathematical description but large enough compared to the molecules to be described by continuous functions. This course is an extension of the course on modeling elastic media in L3 and the course on fluid mechanics (1D).

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This 42-hour course is divided into two identical parts that run in parallel. The first part concerns the study of vibration problems in discrete media and in 1D continuous media (string, beams). The second part concerns the use of variational formulations in order to reformulate the problems studied in L3 in RDM and 3D elasticity. We can then propose optimized approximate solutions. This part of the course allows to make a link between RDM, 3D elasticity and the second semester course of finite elements.

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- Generalized Standard Materials: This course presents a unified framework to describe the thermomechanical behavior of materials. Based on the notions of thermodynamics seen in the preparatory years, it introduces the notion of irreversibility in an extended framework where the nature of the state variables can become tensorial. A link with MMC is essential so that the student understands how a purely mechanical description of continuous media and systems can be completed by a thermodynamic description of the material or the constituents of the medium to be analyzed.

At the end of the course, the student should be able to write the behavioral equations of state and complementary equations associated with a thermomechanical model. He/she should be able to draw up a complete energy balance by calculating in particular the deformation energy, the dissipated energy, the heat sources induced by the thermomechanical couplings

- Heterogeneous Elasticity: In this course, the notion of elasticity is extended to anisotropic media, heterogeneous media (dimensioning of composite materials), and large transformations (entropic elasticity of elastomers).

 - Vibrations and dynamic systems: Basic notions of vibrations for a single degree of freedom modeling, with and without damping. Free vibrations. Forced vibrations. Study of the resonance phenomenon.
Modeling of systems with two degrees of freedom. Resonance and anti-resonance.
Study of systems with a large number of degrees of freedom (e.g. from finite element modeling). Study of eigenmodes.
Dimensioning with respect to dynamic loads.

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This course enables students to apply the key stages of a mechanical design approach, from initial specifications to prototype qualification, to one or more concrete cases dealt with in previous years' industrial projects. It thus supports the year's industrial projects by mobilizing the same skills, but on one or more solved cases, unlike the current projects. It therefore requires the mobilization of various skills acquired in other courses, particularly non-technological ones, in the Master's or Bachelor's program (fundamental principle of dynamics, strength of materials, continuum mechanics, vibrations, finite element simulation) on one or more real mechanisms that students can manipulate and experiment with.

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The internship is carried out in a company or laboratory. During the internship the student must demonstrate:

his understanding of a broad field of basic sciences and his ability to analyze and synthesize them;

its ability to mobilize the resources of a specific scientific and technical field;

his mastery of engineering methods and tools: identification, modeling and resolution of problems, even unfamiliar and incompletely defined ones, the use of computer tools, analysis and design of systems;

its ability to design, implement, test and validate innovative solutions, methods, products, systems and services

its ability to carry out fundamental or applied research activities, to set up experimental devices, to be open to the practice of collaborative work;

ability to find, evaluate and use relevant information;

its ability to take into account the company's challenges: economic dimension, respect for quality, competitiveness and productivity, commercial requirements, economic intelligence;

its ability to take into account the issues of work relations, ethics, responsibility, safety and health in the workplace;

its capacity to integrate into professional life, to integrate into an organization, to lead it and to make it evolve: exercise of responsibility, team spirit, project management, communication with specialists as well as with non-specialists;

His/her ability to work in an international context: mastery of one or more foreign languages and associated cultural openness;

its ability to know itself, to evaluate itself, to manage its competences (in particular in a perspective of lifelong learning), to make its professional choices.

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- Viscoelasticity: The objective of this part is to deepen the modeling of viscoelastic behaviors already seen in the ECUE "Rheology 1" in order to introduce the generalized versions "series" and "parallel" of the Biot model. From a more "material" point of view, the notions of relaxation time spectra are introduced to account for the transformations classically encountered in polymers, as well as the concept of time-temperature equivalence.

 - plasticity: Present the basic plasticity models present in the finite element codes (isotropic and kinematic models). A link is made with the metallurgy course in order to highlight the microstructural events retained during the implementation of macroscopic models. In the same way, the course will be based on the rheology course and on the practical work on materials which have allowed to highlight the notion of threshold and work hardening. The models set up can be used in the projects oriented towards numerical simulation

 - damage : Present the various microscopic manifestations of damage on brittle and ductile materials.
Introduce a thermomechanical theory (Kachanov-Lemaitre) of damage allowing the construction of continuous models adapted to the type of material studied (brittle and ductile materials) as well as to the loading mode (creep, oligo-cyclic fatigue and large number of cycles) The models developed can be used in the option project.

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Description*: Project carried out in a research laboratory or in connection with an industrial problem, during which the student must, alone or in a group, appropriate the problem proposed by the research team, and use the modelling and calculation tools acquired during his/her training to solve it and propose a solution. The student must make a written and oral restitution of his approach and the results obtained.

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This course is an introduction to new design methods associated with additive manufacturing techniques, enabling you to produce a part on a 3D (polymer) printer, from its design on the computer (CAD) in relation to the capabilities of the process, the optimization of its geometry (topological optimization), the preparation and launch of manufacturing, and the finishing stages after printing (completion).

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