Calculation of planar structures

lmeca2520  2019-2020  Louvain-la-Neuve

Calculation of planar structures
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 30.0 h

  This learning unit is not being organized during year 2019-2020.

Doghri Issam;
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 so-called 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.
Some rather simple problems will also be solved analytically in order to better understand the theory.

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:
  • AA1.1, AA1.2, AA1.3
  • AA2.1, AA2.2, AA2.3
  • AA3.1, AA3.2
  • AA5.1, AA5.2, AA5.3
  • AA6.1, AA6.2
Analytical and numerical modeling of two-dimensional problems in linear elasticity:
  • plane strain;
  • plane stress;
  • bending of plates.

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”.
Chapitre 1 : Plane strain and plane stress in Cartesian coordinates.
Chapitre 2 : Plane strain and plane stress in cylindrical coordinates.
Chapitre 3 : Kirchhoff-Love plate theory in Cartesian coordinates.
Chapitre 4 : Kirchhoff-Love plate theory in cylindrical coordinates.
Chapitre 5 : Reissner-Mindlin 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 semi-infinite 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, post-processing and visualization of computation results).
Faculty or entity

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Master [120] in Mechanical Engineering

Master [120] in Architecture and Engineering

Master [120] in Civil Engineering

Master [120] in Electro-mechanical Engineering

Master [120] in Chemical and Materials Engineering