Mechanics

This 42-hour course provides the basics of continuum mechanics: we study movements, deformations, and stress fields within media that are considered from a macroscopic point of view, as opposed to a corpuscular description. More specifically, we analyze these physical phenomena by describing them from a mathematical point of view.

Acquire the basics of physical modeling of problems arising in engineering sciences such as structural analysis, manufacturing processes, biomechanics, fluid mechanics, civil engineering, and the design of new materials.

Have completed a bachelor's degree in mathematics

Recommended prerequisites: Have taken a basic course in rigid body mechanics, if possible.

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

• Continuum Mechanics
  Conservation law. Stress tensor.
  Study of the stress tensor
• Linear elasticity equations
  Classification and variational formulations of elasticity problems
• Concepts of incompressible fluid mechanics: Fluid kinematics, acceleration, vorticity, incompressibility, and conservation of volume. Fluid dynamics: Laws of behavior, 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 calculation code for simple flows.

Hourly volumes:

            CM: 21

            TD: 21

            TP:

            Land: