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.
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
Necessary pre-requisites
Have completed a Bachelor's degree in mathematics
Recommended Prerequisites: Completion of a basic course in rigid media mechanics if possible.
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.
Additional information
Hourly volumes:
CM : 21
TD : 21
TP:
Terrain: