• ECTS

    7 credits

  • Component

    Faculty of Science

Description

This 42-hour course gives the basic elements of continuum mechanics: we study the motions, deformations and stress fields within media that we consider from a macroscopic point of view, as opposed to a corpuscular description. More precisely, we analyze these physical phenomena by describing them from a mathematical point of view.

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Objectives

Acquire the basics of physical modeling of engineering problems such as structural design, manufacturing processes, biomechanics, fluid mechanics, civil engineering, design of new materials

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Necessary pre-requisites

Have completed a Bachelor's degree in mathematics

 

 

Recommended Prerequisites: Completion of a basic course in rigid media mechanics if possible.

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Syllabus

The course is divided, in a very classical way, into three parts:

  • Kinematics of Continuous Media
    Conservation law. Stress tensor.
    Study of the stress tensor
  • Linear elasticity equations
    Classification and variational formulations of elasticity problems
  • Notions of incompressible fluid mechanics: Kinematics of fluids, acceleration, vorticity, incompressibility and conservation of volume. Fluid dynamics: Behavior laws, viscosity, Newtonian fluids, Navier Stokes equations, scaling and symmetries. Some analytical solutions: Couette, Poiseuille. Stokes equations and weak formulation with various boundary conditions. Existence, uniqueness and regularity by the Lax Milgram Babuska theorem. Use of finite element code for simple flows.
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Additional information

Hourly volumes:

            CM : 21

            TD : 21

            TP:

            Terrain:

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