Mechanics

This 42-hour course covers the fundamentals of continuum mechanics: it examines motion, deformation, and stress fields within media considered from a macroscopic perspective, as opposed to a particle-based description. More specifically, these physical phenomena are analyzed by describing them from a mathematical perspective.

Acquire the fundamentals of physical modeling for problems in engineering disciplines 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:

• Kinematics of Continuous Media
  Conservation Law. Stress Tensor.
  Study of the Stress Tensor
• Equations of Linear Elasticity
  : Classification and Variational Formulations of Elasticity Problems
• Concepts in incompressible fluid mechanics: Fluid kinematics, acceleration, vorticity, incompressibility, and conservation of volume. Fluid dynamics: Laws of behavior, viscosity, Newtonian fluids, the Navier-Stokes equations, scaling, and symmetries. Some analytical solutions: Couette, Poiseuille. Stokes’ equations and the weak formulation with various boundary conditions. Existence, uniqueness, and regularity via the Lax–Milgram–Babuska theorem. Use of finite element code for simple flows.

Hourly volumes:

            CM: 21

            TD: 21

            Practical Work:

            Lot: