5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Doghri Issam;
Language
English
Main themes
 The objective of the course is to show analytically in simple cases and numerically how to model and solve an important class of socalled planar structures, i.e. such that their mechanical problem is reduced to two space dimensions.
 The problems involve " long " solids under plane strain, " thin " solids under plane stress and thin or thick plates under bending loads.
 For each class of problems, appropriate formulations will be developed, together with their finite element discretization, in view of their numerical resolution using a specialized software.
Aims
At the end of this learning unit, the student is able to :  
1  In consideration of the reference table AA of the program "Masters degree in Mechanical Engineering", this course contributes to the development, to the acquisition and to the evaluation of the following experiences of learning:
Analytical and numerical modeling of twodimensional problems in linear elasticity:

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
Chapitre 1 : Plane strain and plane stress in Cartesian coordinates.
Chapitre 2 : Plane strain and plane stress in cylindrical coordinates.
Chapitre 3 : KirchhoffLove plate theory in Cartesian coordinates.
Chapitre 4 : KirchhoffLove plate theory in cylindrical coordinates.
Chapitre 5 : ReissnerMindlin plate theory.
Chapitre 6 : Finite element formulations of plate theories.
Chapitre 2 : Plane strain and plane stress in cylindrical coordinates.
Chapitre 3 : KirchhoffLove plate theory in Cartesian coordinates.
Chapitre 4 : KirchhoffLove plate theory in cylindrical coordinates.
Chapitre 5 : ReissnerMindlin plate theory.
Chapitre 6 : Finite element formulations of plate theories.
Teaching methods
Travaux pratiques :
 Resolution of several relatively simple problems dealing usually with direct applications of the theory (e.g., tube under inner and outer pressures, stress concentration in a plate with a small circular hole, force on the straight edge of a semiinfinite plate, bending of a circular plate under axisymmetric loading, etc.)
 Use of a finite element numerical software, in order to understand the main steps of the method (geometry definition, input of material data and other problem parameters, space and time discretization, solver algorithms, postprocessing and visualization of computation results).
Online resources
Faculty or entity
MECA
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Electromechanical Engineering
Master [120] in Mechanical Engineering
Master [120] in Civil Engineering
Master [120] in Chemical and Materials Engineering
Master [120] in Architecture and Engineering