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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The aim of this course is to prepare students for professional interviews by giving them the keys to making the most of their past experience.

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

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This teaching unit introduces students to :

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

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

Class sessions will be supplemented by a company visit, as well as by a methodological approach based on concretecase studies.

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This 42-hour course is divided into two parts (1/3, 2/3) to give the basics of heat transfer and fluid mechanics (3D). Fluids will be considered as continuous media. A particle is an element of volume infinitesimally small for mathematical description, but large enough relative to molecules to be described by continuous functions. This course extends the L3 course on modeling elastic media, as well as the 1D fluid mechanics course.

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This 42-hour course is divided into two identical parts running in parallel. The first part deals with the study of vibration problems in discrete media and in 1D continuous media (rope, beams). The second involves the use of variational formulations to reformulate the problems studied in L3 in RDM and 3D elasticity. This enables us to propose optimized approximate solutions. This part of the course provides a link between RDM, 3D elasticity and the second-semester finite element course.

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- Generalized Standard Materials: This ECUE presents a unified framework for describing the thermomechanical behavior of materials. Building on the notions of thermodynamics introduced in the preparatory years, it introduces the notion of irreversibility in a broader framework where the nature of 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 complemented by a thermodynamic description of the material or constituents of the medium to be analyzed.

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

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

 - Vibration and dynamic systems: Vibration basics for 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. resulting from finite element modeling). Study of eigenmodes.
Sizing for 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, students must demonstrate :

understanding of a wide range of basic sciences and the associated ability to analyze and synthesize;

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

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

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

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

its ability to find, evaluate and exploit relevant information;

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

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

its ability to fit into professional life, to integrate into an organization, to lead it and to help it evolve: exercising responsibility, team spirit, project management, communication with specialists and non-specialists alike;

ability to work in an international context: mastery of one or more foreign languages and cultural awareness;

the ability to know oneself, to self-assess, to manage one's skills (particularly in the context of lifelong learning), and to make professional choices.

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- Viscoelasticity: The aim of this section is to extend the modeling of viscoelastic behavior already covered in ECUE "Rheology 1", in order to introduce the generalized "series" and "parallel" versions of Biot's 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 used in finite element codes (isotropic and kinematic models). A link is made with the metallurgy course in order to highlight the microstructural events selected when setting up macroscopic models. Similarly, the course will be based on the rheology course and materials practical work, which have highlighted the notion of threshold and strain hardening. The models developed can be used in numerical simulation projects.

 - damage : Present the various microscopic manifestations of damage in brittle and ductile materials.
Introduce a thermomechanical theory (Kachanov-Lemaitre) of damage, enabling the construction of continuous models adapted to the type of material studied (brittle and ductile materials), as well as to the loading mode (creep, low-cycle and high-cycle fatigue). 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 modeling and calculation tools acquired during his/her training to solve it and propose a solution. Students are required to give a written and oral presentation of their approach and the results obtained.

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This course is an introduction to the 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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