This course is an introduction to the mechanics of the deformable bodies within the framework of the linear elasticity and establishes foundations necessary for the sizing and for the calculation of structures generally.
It thus defines at first the notions of stresses and strains in a continuous material. The laws of behavior (mainly case of the elasticity) allow to connect these two characteristics. It lands then briefly in the notions of energy of deformation and of criterion of elastic limit.
Finally, it presents the putting in equations (and the methods of analytical resolution associated) of a continuous problem from the Fundamental Principle of Statics (equation of Lamé-Navier, Airy functions) or of an energy approach as the Variational methods.

Learning objectives

The objective of this teaching is to help the student to apply bases necessary for the study of the deformable solid, approached during its Prerequisite courses.

Learning context

Course materials

Handouts of de courses and execises

Bibliography
Résistance Des Matériaux; Tome I. Théorie Elémentaire Et Problèmes Timoshenko DUNOD
Résistance Des Matériaux; Tome 2. Théorie Développée Et Problèmes Timoshenko DUNOD
Résistance Des Matériaux; M. Kerguignas G. Caignaert DUNOD UNIVERSITE

Prerequisites

- Matrix algebra and vectorial analysis
- Mechanics of the rigid bodies
- lessons of experimental mechanics; mechanics of materials; general mechanics

Course content

Chapter 1: tensor of the stresses
External and internal efforts. Equations of balance.
Stress Vector. Stress Tensor.
Main stresses and main directions. Mohr's circles.

Chapter 2: tensor of the strains
Displacement and deformation of an elementary volume.
Small transformations.
Compatibility Equations.

Chapter 4: Strain energy - Elastic Limit Criteria
Elastic potential.
Equivalent strains.
Limit of validity of the elasticity.

Chapter 5: methods of solving - Applications
Fundamental principle of statics.
the Variational methods.
Planar Elasticity.

Tutorial classes
Exercises familiarize with the notions of constraints and local deformations strains in a body, and the relations which connect them, and translate the balance of a deformable body thanks to the local equation of balance and the expression of the limit conditions.
The last tutorial classes present the analytical resolution of several two-dimensional problems of elasticity (or three-dimensional), by the use of different methods, specific to the geometry, or adapted to the nature of the solution looked (stressess, displacements), within the framework of the flat élasto-statics, but also in thermo-elasticity or in élasto-dynamics.
Practical class
Application of the notions and the methodology of resolution of Elasticity, from models of Laboratory, for two classic examples of elasticity: beam Bends. Thick cylinder.
Both sessions are used, to familiarize the students in the use of strains gages to measure the distortions, and the use of a Wheatstone bridge.

Personal work

Regular work, and to redo the in class solved exercises

Exams

Label (French)

Label (English)

Elasticité

Elasticity

Exam description

Written test: solving of a simple problem of mechanics of the deformable bodies(equation of balance and limits conditions ). (2 hours)