Mechanical engineering

This 42-hour course introduces the basics of continuum mechanics: we study motions, deformations and stress fields in 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 mathematically.

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

Have completed a Bachelor's degree in mathematics

Recommended prerequisites: A basic course in rigid media mechanics, if possible.

The course is classically divided into three parts:

• Kinematics of Continuous Media
  Conservation law. Stress tensor.
  Stress tensor study
• Linear elasticity equations
  Classification and variational formulations of elasticity problems
• Notions of incompressible fluid mechanics: fluid kinematics, 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 Lax Milgram Babuska theorem. Use of finite element codes for simple flows.

Hourly volumes :

            CM: 21

            TD : 21

            TP :

            Terrain :