Calculations and Simulations in Mechanical Engineering

The goal 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 introduction is presented within the framework of linear elasticity and small perturbations in statics. Building on prerequisites in mathematics and solid mechanics, the principle of discretization is first addressed through the Ritz and Galerkin approaches for one-dimensional media. Next, the issue of numerical integration is addressed using Gauss’s method. Meshing and the validation of computational models are then discussed in the context of surface modeling with 2D elements. Finally, these concepts will be used to establish the complete formalism of the finite element method for bar and beam elements, followed by triangular elements. A practical application of these important theoretical concepts is carried out using industrial simulation software (ANSYS) during lab sessions and a project.

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The purpose of this course unit is to prepare students for job interviews by providing them with the tools they need to highlight their past experiences.

This training is conducted using mock interview exercises based on actual job postings.

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This course introduces students to:

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

- corporate marketing, from market research to operational marketing. The marketing approach will be directly applied as part of the industrial design project led by the student teams.

Class sessions will be supplemented by a company visit, as well as a methodological approach involvingthe analysis of real-worldcase studies.

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: This 42-hour course is divided into two parts (1/3, 2/3) to provide the fundamentals of heat transfer and fluid mechanics (3D). Fluids will be treated as continuous media. A “particle” is defined as a volume element that is infinitely small for mathematical description but large enough relative to molecules to be described by continuous functions. This course builds upon the L3 course on modeling elastic media as well as the course on fluid mechanics (1D).

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This 42-hour course is divided into two identical parts that run concurrently. 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 into RDM and 3D elasticity.  This approach allows us to propose optimized approximate solutions. This part of the course establishes a connection 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 thermodynamic concepts covered in the preparatory years, the goal is to introduce the concept of irreversibility within a broader framework where the nature of the state variables can become tensor-based. A connection to the 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 the constituents of the medium being analyzed.

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

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

 - Vibrations and Dynamic Systems: Basic concepts in vibrations for modeling a single degree of freedom, with and without damping. Free vibrations. Forced vibrations. Study of the phenomenon of resonance.
Modeling of systems with two degrees of freedom. Resonance and antiresonance.
Study of systems with a large number of degrees of freedom (e.g., resulting from finite element modeling). Study of eigenmodes.
Design for dynamic loads.

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This course unit allows students to apply the key steps of a mechanical design process—from the initial specifications to prototype qualification—to one or more real-world cases addressed in previous years as part of industrial projects. It thus supports the current year’s industrial projects by drawing on the same skills, but in the context of one or more cases that have already been resolved, as opposed to ongoing projects. It therefore requires students to apply the various skills acquired in other course units—particularly non-technical ones—from either the Master’s or Bachelor’s programs (fundamentals of dynamics, strength of materials, continuum mechanics, vibrations, finite element simulation) to one or more real-world mechanisms that students can handle and experiment with.

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

his or her understanding of a broad range of basic sciences and the associated analytical and synthesis skills;

their ability to draw on resources from a specific scientific and technical field;

his or her mastery of engineering methods and tools: identifying, modeling, and solving problems—even those that are unfamiliar or incompletely defined—using computer tools, and analyzing and designing systems;

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

their ability to conduct research—whether basic or applied—to set up experimental designs, and to embrace collaborative work;

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

's ability to take into account the company's challenges: economic factors, quality standards, competitiveness and productivity, business requirements, and business intelligence;

their ability to address issues related to workplace relationships, ethics, accountability, and occupational safety and health;

: the ability to enter the workforce, integrate into an organization, lead it, and drive its development—including exercising responsibility, demonstrating teamwork, managing projects, serving as a project owner, and communicating effectively with both specialists and non-specialists;

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

their ability to understand themselves, to self-assess, to manage their skills (particularly from the perspective of lifelong learning), and to make career choices.

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- Viscoelasticity: The objective of this section is to delve deeper into the modeling of viscoelastic behaviors already covered in the ECUE “Rheology 1” course in order to introduce the generalized “series” and “parallel” versions of the Biot model. From a more “materials-oriented” perspective, the concepts of relaxation time spectra are introduced to account for the transformations typically observed in polymers, as well as the concept of time-temperature equivalence.

 - Plasticity: Present the basic plasticity models used in finite element analysis codes (isotropic and kinematic models). A connection is made with the metallurgy course to highlight the microstructural phenomena considered when developing macroscopic models. Similarly, the course will build on the rheology course and the materials lab sessions, which helped clarify the concepts of yield threshold and work hardening. The models developed can be used in projects focused on numerical simulation.

 - Damage: Describe the various microscopic manifestations of damage in brittle and ductile materials.
Introduce a thermomechanical theory (Kachanov-Lemaitre) of damage that allows for the development of continuous models suited to the type of material under study (brittle and ductile materials) as well as the loading mode (creep, low-cycle fatigue, and high-cycle fatigue). The models developed may be used in the elective project.

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Description*: A project carried out in a research laboratory or in connection with an industrial problem, during which the student, either individually or in a group, must engage with the problem proposed by the research team and use the modeling and computational tools acquired during their training to solve it and propose a solution. The student must present a written and oral report on their approach and the results obtained.

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This course provides an introduction to new design methods associated with additive manufacturing techniques, enabling students to create a part using a 3D printer (polymer-based). The course covers the entire process, from computer-aided design (CAD) tailored to the capabilities of the process, to the optimization of the part’s geometry (topological optimization), the preparation and initiation of the manufacturing process, and the post-printing finishing steps.

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This course unit applies to the “Innovative Mechanics Project.” The goal is to provide students with the tools to simulate the process of starting a business based on the product or product line developed as part of the innovative project.

This learning unit is divided into:

a course taught by professionals in the field of entrepreneurship

Consultations provided by professionals to guide students (in groups of up to three) through a simulation of starting their own business.

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This course provides a general introduction to 1) the physics and mechanics of granular media and 2) their modeling using discrete methods (DEM). The multiscale nature of a granular material is discussed, ranging from the microscopic scale (contact interactions) to the macroscopic scale (structural scale). A phenomenological description of macroscopic behavior as well as microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micromechanical models and scale-change approaches based on dimensionless analyses, averaged quantities, stress transmission, and the presence of anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Numerical approaches such as discrete methods (Discrete Element Methods, DEM), regular methods (Molecular Dynamics), and non-regular methods (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be applied to simple examples using the LMGC90 computational code.

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This course is common to both the CSIM and Biomechanics tracks. It combines skills in the mechanics of rigid bodies and imaging. It applies to problems in biomechanics, robotics, and many other fields related to motion analysis, such as “motion capture” for video games. It consists of a theoretical component—including lectures and tutorials—and a practical component—laboratory sessions conducted in collaboration with the STAPS department.

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The purpose of this course unit is to prepare students for job interviews by providing them with the tools they need to highlight their past experiences.

This training is conducted using mock interview exercises based on actual job postings.

Labor law here focuses on an analysis of the main provisions of an employment contract, including, in particular, the obligations of the employee, the obligations of the employer, and the termination of the employment relationship.

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Although natural composite materials have been in use for thousands of years, the high-tech applications of advanced composites have only been used in the aerospace industry for the past fifty years. Applications are becoming increasingly diverse: from aircraft structures and hydrogen tanks to tennis rackets and boats. The objective of this course is to analyze and design structures made of laminated composite materials using industrial simulation software. To this end, an overview of the various components of petrochemical-based and natural composites is provided. Next, the manufacturing processes are discussed. Finally, a theoretical and applied study of laminated composites is conducted. A practical application of these important theoretical concepts is carried out using industrial simulation software (ANSYS) during lab sessions and a project.

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This course is a continuation of the “Advanced Numerical Simulation” module. It is a project-based module that focuses on computational aspects, similar to what is done in engineering design firms.

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Chapter 1: Large Deformations and Numerical Analysis

Chapter 2: Numerical Solutions to Steady-State and Transient Problems (Elastoplasticity, Contact, Friction)

Chapter 3: Numerical Solutions in Transient Dynamics and Modal Analysis

The lectures are supplemented by application-based tutorials, and the lab sessions are conducted using ANSYS software.

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Field measurements are increasingly used in engineering, particularly in mechanical engineering. The objective of this module is to introduce the fundamentals of various imaging methods using image interpretation models of increasing complexity.

We begin by defining the operating principles of imaging devices, then present some tools from mathematical morphology to extract statistical information about geometric quantities.

We then discuss infrared thermography methods through two interpretive models: camera calibration and thermal problem inversion to identify heat sources.

Finally, image correlation methods are presented, with an emphasis on the various underlying interpretive models (camera, transformation, conservation of optical flux, likelihood criterion).The course concludes with a comparison between experimental measurements and a numerical model using a finite-element model registration method. The theoretical lectures are supplemented by laboratory sessions that allow students to apply the processing methods and illustrate the influence of the main analysis parameters.

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This course is of paramount importance to the program. It involves applying all the knowledge and skills acquired throughout the program by carrying out a long-term scientific project.

View the full page

View the full page

This course unit applies to the “Innovative Mechanics Project.” The goal is to provide students with the tools to simulate the process of starting a business based on the product or product line developed as part of the innovative project.

This learning unit is divided into:

a course taught by professionals in the field of entrepreneurship

Consultations provided by professionals to guide students (in groups of up to three) through a simulation of starting their own business.

View the full page

This course provides a general introduction to 1) the physics and mechanics of granular media and 2) their modeling using discrete methods (DEM). The multiscale nature of a granular material is discussed, ranging from the microscopic scale (contact interactions) to the macroscopic scale (structural scale). A phenomenological description of macroscopic behavior as well as microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micromechanical models and scale-change approaches based on dimensionless analyses, averaged quantities, stress transmission, and the presence of anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Numerical approaches such as discrete methods (Discrete Element Methods, DEM), regular methods (Molecular Dynamics), and non-regular methods (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be applied to simple examples using the LMGC90 computational code.

View the full page

This course is common to both the CSIM and Biomechanics tracks. It combines skills in the mechanics of rigid bodies and imaging. It applies to problems in biomechanics, robotics, and many other fields related to motion analysis, such as “motion capture” for video games. It consists of a theoretical component—including lectures and tutorials—and a practical component—laboratory sessions conducted in collaboration with the STAPS department.

View the full page

The purpose of this course unit is to prepare students for job interviews by providing them with the tools they need to highlight their past experiences.

This training is conducted using mock interview exercises based on actual job postings.

Labor law here focuses on an analysis of the main provisions of an employment contract, including, in particular, the obligations of the employee, the obligations of the employer, and the termination of the employment relationship.

View the full page

Although natural composite materials have been in use for thousands of years, the high-tech applications of advanced composites have only been used in the aerospace industry for the past fifty years. Applications are becoming increasingly diverse: from aircraft structures and hydrogen tanks to tennis rackets and boats. The objective of this course is to analyze and design structures made of laminated composite materials using industrial simulation software. To this end, an overview of the various components of petrochemical-based and natural composites is provided. Next, the manufacturing processes are discussed. Finally, a theoretical and applied study of laminated composites is conducted. A practical application of these important theoretical concepts is carried out using industrial simulation software (ANSYS) during lab sessions and a project.

View the full page

This course is a continuation of the “Advanced Numerical Simulation” module. It is a project-based module that focuses on computational aspects, similar to what is done in engineering design firms.

View the full page

Chapter 1: Large Deformations and Numerical Analysis

Chapter 2: Numerical Solutions to Steady-State and Transient Problems (Elastoplasticity, Contact, Friction)

Chapter 3: Numerical Solutions in Transient Dynamics and Modal Analysis

The lectures are supplemented by application-based tutorials, and the lab sessions are conducted using ANSYS software.

View the full page

Field measurements are increasingly used in engineering, particularly in mechanical engineering. The objective of this module is to introduce the fundamentals of various imaging methods using image interpretation models of increasing complexity.

We begin by defining the operating principles of imaging devices, then present some tools from mathematical morphology to extract statistical information about geometric quantities.

We then discuss infrared thermography methods through two interpretive models: camera calibration and thermal problem inversion to identify heat sources.

Finally, image correlation methods are presented, with an emphasis on the various underlying interpretive models (camera, transformation, conservation of optical flux, likelihood criterion).The course concludes with a comparison between experimental measurements and a numerical model using a finite-element model registration method. The theoretical lectures are supplemented by laboratory sessions that allow students to apply the processing methods and illustrate the influence of the main analysis parameters.

View the full page

This course is of paramount importance to the program. It involves applying all the knowledge and skills acquired throughout the program by carrying out a long-term scientific project.

View the full page

View the full page