M1 - Calculations and Simulations in Mechanical Engineering

The aim of this course is to introduce students to the finite element method applied to one-, two-, and three-dimensional problems in engineering and applied science. This introduction is given in the context 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 Ritz and Gallerkine approaches for one-dimensional media. Next, the issue of numerical integration is approached using the Gauss method. Meshing and validation of calculation models are then addressed during the study of surface modeling with 2D elements. Finally, these concepts will be used to implement the complete formalism of the finite element method in the context of bar and beam elements, then triangle-type elements. A practical application of these important theoretical concepts 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 job interviews by giving them the keys to promoting their past experiences.

This training is based on interview simulation games built on the basis of existing job offers.

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This teaching unit introduces students to:

- to management within the company, presenting the company as an economic and legal entity on the one hand, and addressing the strategic approach as a whole on the other.

- marketing within the company, from market research to operational marketing. The marketing approach will be directly applied within the framework of the industrial creation project led by the student teams.

Classes will be supplemented by a company visit and a methodological approachto studying real-lifecase studies.

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

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

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- Generalized Standard Materials: This ECUE presents a unified framework for describing the thermomechanical behavior of materials. Building on the concepts of thermodynamics covered in preparatory years, it introduces the concept of irreversibility in a broader framework where the nature of state variables can become tensorial. A link with MMC is essential so that students understand how a purely mechanical description of continuous media and systems can be supplemented 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 in particular the deformation energy, the dissipated energy, and the heat sources induced by thermomechanical couplings.

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

 - Vibrations and dynamic systems: Basic concepts of vibrations for single-degree-of-freedom modeling, with and without damping. Free vibrations. Forced vibrations. Study of the phenomenon of resonance.
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 natural modes.
Dimensioning with respect to dynamic stresses.

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

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The internship takes place in a company or laboratory. During the internship, students must demonstrate:

their understanding of a broad range of fundamental sciences and their associated analytical and synthesis skills;

their ability to mobilize resources from 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; use of computer tools; analysis and design of systems;

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

their ability to carry out fundamental or applied research, set up experimental devices, and embrace collaborative working practices;

their ability to find relevant information, evaluate it, and use it;

ability to take into account the challenges facing the company: economic dimension, quality compliance, competitiveness and productivity, commercial requirements, economic intelligence;

their ability to take into account issues relating to workplace relations, ethics, responsibility, and occupational health and safety;

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

ability to work in an international context: proficiency in one or more foreign languages and associated cultural openness;

their ability to know themselves, to self-assess, to manage their skills (particularly with a view to lifelong learning), and to make career choices.

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- Viscoelasticity: The aim of this section is to explore in greater depth the modeling of viscoelastic behaviors already covered in the "Rheology 1" ECUE in order to introduce the generalized "series" and "parallel" versions of the Biot model. From a more "material" perspective, the concepts of relaxation time spectra are introduced to account for the transformations typically encountered in polymers, as well as the concept of time-temperature equivalence.

 - Plasticity: Present the basic plasticity models used in finite element calculation codes (isotropic and kinematic models). A link is made with the metallurgy course in order to highlight the microstructural events selected when setting up the macroscopic models. Similarly, the course will draw on the rheology course and the materials practicals, which highlighted the concepts of threshold and work hardening. The models set up can be used in projects focused on numerical simulation.

 - Damage: Present the various microscopic manifestations of damage on brittle, ductile materials.
Introduce a thermomechanical theory (Kachanov-Lemaitre) of damage that can be used to construct continuous models adapted to the type of material studied (brittle, ductile materials) and the loading mode (creep, oligo-cyclic fatigue, 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 issue, during which the student must, alone or in a group, take ownership of the problem proposed by the research team and use the modeling and calculation tools acquired during their training to solve it and propose a solution. The student must provide a written and oral report on their approach and the results obtained.

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This EU is an introduction to new design methods associated with additive manufacturing techniques used to produce a part on a 3D printer (polymer), from its creation on a computer (CAD) in line with the capabilities of the process, to the optimization of its geometry (topological optimization), the preparation and launch of manufacturing, and the finishing stages after printing (post-processing).

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