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I4GCRM11 (6 ECTS credits)
Advanced mechanics : non-linear and numerical computation
Objectives :
At the end of this module, the student will have understood and be able to explain (main concepts) :
Linear mechanics and its usage
The different phenomena of buckling at different scales: cross-section,
members, global structure
Plasticity calculations for structures (plastic hinge method)
Viscoelastic analysis, viscoelasticity models, application to creep, stress
relaxation and calculation of long-term strain
Modelling using Finite Element Method
Elements properties: beams, plates and shells, solids
The student will be able to:
Calculate the global buckling of structures
Calculate the local buckling of structural members
Calculate the ultimate load bearing capacity using the plastic hinge method
Design a structure using Finite Element Software
Description :
Programme (detailed contents) :
- Usage limitations of first-order analysis (linear analysis)
- Non-linear geometry
Local buckling: buckling, lateral buckling, lateral torsional buckling
Global buckling: Rayleigh-Timoshenko method
- Non-linear behaviour of materials
Yielding: constitutive laws and criteria, cross-section yielding, limit analysis of
structures
Viscoelasticity: constitutive laws, stress relaxation and creep. Long term strain
calculation using Laplace transform
- Finite Element Method
Variational formulation, Principe of virtual power
Discretisation
Assembly of system matrices and computation
Element properties: beams, plates and shells, solids
- Stationary analysis, dynamic analysis (eigenvalue calculation), buckling
Organisation:
Lectures, tutorials, individual project
Assessment :
How do you assess that the objectives have been reached ?
Traditional assessment for main concepts,
Written report for individual tutorial.
How does your assessment system help the student to reach the objectives ?
Completing the individual project requires the understanding of the methods and models presented in the course.
Assessment method : Written exam, Report
Number of hours : 41.25h (lectures), 18.75h (tutorials), 30h (Project), 60h (Personal work)
Prerequisites :
Solids and linear structure mechanics.
Materials resistance.
Unit of study coordinator : Raoul François
Semester : 1
Bibliography :
Comportement mécanique des matériaux, élasticité et plasticité ; D. François, A. Pineau, A. Zaoui ; Hermés.
Comportement mécanique des matériaux, viscoplasticité, endommagement mécanique, mécanique de la rupture, mécanique du contact ; Hermés.
Mécanique non linéaire des matériaux ; Jacques Besson, Georges Caillebaud, Jean-Louis Chaboche, Samuel Forest ; Hermés, 2001.
La maîtrise du calcul en mécanique linéaire et non linéaire, Pierre Ladevèze, Jean-Pierre Pelle ; Hermés 2001.
Modélisation mécanique des structures, Christian Decolon, Michel Borel, Hermés, 2000.
Théorie de la stabilité élastique, S.P. Timoshenko, Dunod, 1966.
Modélisation des structures par éléments finis, Tome 1,2,3 ; J-L. Batoz, G. Dhatt.
La modélisation des ouvrages, Michel Prat & al ; Hermés.
Institut des Sciences Appliquées de Toulouse
http://odf.insa-toulouse.fr/