L3 - CUPGE Mechanical Engineering

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The objective of this course is to provide an introduction to numerical tools for solving partial differential equations arising from various fields of engineering. We will cover the spectral method as applied to the heat diffusion equation in a rod and the development of codes based on this technique. In particular, students will be required to implement this method in Python in order to gain a foundation in the language and version control tools. Student assignments will be produced using the LaTeX typesetting system.  

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The focus is on the performance and limitations of computational methods in engineering so that students will be able to apply them correctly “in real-world situations.” This real-world application is certainly the most challenging aspect of this introduction to scientific computing, as it requires not only a certain understanding of physics but also a broader perspective on mathematical modeling, as well as a basic level of computer skills.

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In the first part: a more in-depth look at the basic concepts of differential calculus covered in the second year.

In the second part: introduce the qualitative analysis of differential equations.

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Materials strength (RdM) is a specific branch of continuum mechanics that enables the calculation of stresses and strains in slender structures made of various materials (machinery, mechanical engineering, building, and civil engineering). It involves a 1D static model of a deformable solid treated as a beam connected to a frame and subjected to external mechanical loads.

The RdM makes it possible to reduce the study of a structure’s global behavior (the relationship between loads—forces or moments—and displacements) to that of the local behavior of its constituent materials (the relationship between stresses and strains). Mechanical stresses can be viewed as the “cohesive forces ” within the material. The strains of a physical object are observed as changes in its dimensions or overall shape.

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The objective of this first module on fluid mechanics is to provide a basic understanding of the behavior of industrial fluids (air, water, hydraulic fluid) in order to size simple systems involving fluids in static or dynamic conditions (flow rates, pressure, velocity, pressure drops, etc.). The focus is on the study and design of hydraulic systems.

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Rheology is the study of the deformation and flow of materials under the influence of an applied mechanical load. In the field of materials science, this discipline is particularly relevant to the following areas:

            - Viscoelasticity

            - Plasticity

            - Viscoelasticity

            - Non-Newtonian fluids

In practice, rheology makes it possible to characterize the macroscopic mechanical properties of materials whose behavior cannot be described by classical theories of elastic solids and Newtonian fluids (with constant viscosity). Such materials can thus be considered to exhibit behavior that lies between that of a solid and a fluid, and between elastic and viscous behavior.

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This course aims to introduce the fundamentals of physical hydrodynamics. The kinematic aspects are covered first: Eulerian and Lagrangian formalisms, analysis of the motion of a fluid volume element, introduction to the stream and potential velocity functions, and applications to various types of flows. In the next section on fluid dynamics, we derive Euler’s equation and Bernoulli’s equation for the flow of ideal fluids, followed by the Navier-Stokes equation describing the flow of Newtonian viscous fluids. This section will lead us to define the stress tensor as well as the Reynolds number, which allows us to determine whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids: displacement field, strain tensor, and deformation tensor.

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The course, which combines computational science and variational methods in mechanics, is designed to model simple physical equations and implement numerical methods to solve them

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Acquire a basic understanding of numerical methods for differential equations

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Language lab courses designed to develop the five language skills;

Listening Comprehension & Speaking

Reading Comprehension & Writing

Oral Interaction

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• read a technical drawing of moderate difficulty
• identify standard mechanical components on a drawing
• Identify how a moderately complex mechanical system works based on a general diagram
• Draw a part from multiple views, following the rules of projection
• Identify and draw the intersections of a cylinder and a plane, two cylinders, a plane and a cone, and a cylinder and a cone
• draw cross-sectional views and sections
• Extract a part from a medium-difficulty assembly drawing
• use of the basic functions of SolidWorks software (Part, Assembly, and Drawing modes)

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Research and Development (R&D) is both the result of teamwork and individual talent, all in the service of innovation (applied research) and knowledge (basic research). The topics are diverse and varied, but a certain methodology is necessary to address any R&D challenge.

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The objective of this course is to model solid continuous media, focusing initially on elastostatics under the assumption of small perturbations. In this course, we will explore the application of the fundamental principle of statics to deformable solids. To this end, the following concepts are introduced: tensors and tensor fields, tensor algebra and analysis, boundary value problems, the fundamental principle of statics, and the principle of virtual powers. Techniques for the analytical solution of classical problems and energy-based approaches will be covered. This course is fundamental to the education of students in mechanics, whether they are pursuing careers in design and engineering or in R&D.

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Project assigned to a group of two to three students, supervised by a tutor. Weekly meetings are held to monitor progress and provide assistance with writing a report and preparing an oral presentation. The project spans one semester and concludes with the submission of a report and an oral defense.

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