Structural Analysis

5-year combined undergraduate / graduate Engineering programs

General Data
Academic program	General Engineering Program			:
Type d'EC	Classes
Lectures : 20h00 Lab Work : 16h00 Total duration : 50h00	Status :	Period : SEMESTER 6	Education language : French

Learning Outcomes
"Being able to choose the physical parameters and the analysis parameters which influence the results of a computation of stresses and displacements by finite elements, according to whether the structure is isostatic or hyperstatic, linear or nonlinear, and that it is stressed beyond the elastic limit of the material or not. Using finite element calculation software wisely in order to obtain stress and displacement values in accordance with reality, whatever the context of the study. "

Learning Outcomes

"Being able to choose the physical parameters and the analysis parameters which influence the results of a computation of stresses and displacements by finite elements, according to whether the structure is isostatic or hyperstatic, linear or nonlinear, and that it is stressed beyond the elastic limit of the material or not.
Using finite element calculation software wisely in order to obtain stress and displacement values in accordance with reality, whatever the context of the study.
"

Content
The course is divided into two parts. A section "Strength of Materials" which exposes through courses and exercises, the physical parameters which influence the behavior of a structure. This part contains the following chapters: - calculations of displacements in beam structures, - study of the particularities of hyperstatic structures compared to isostatic structures, - introduction to plastic calculation, notions of plastic adaptation and plastic ruin, - introduction to elastic instabilities and geometric nonlinearities, example of buckling of compressed beams. A section " Finite Element analysis" which exposes through courses and comparisons of results of calculations, the parameters of analysis whose choices must be reasoned. This part contains the following chapters: - Finite Element method: notion of approximation and influence of the mesh, - types of elements, - boundary conditions - analysis options. Practical work is associated with each of these parts. The practical work associated with the "Strength of Materials" part includes experimental verifications, in addition to finite element simulations. These pratical works are: - equations of a nonlinear problem (flexible elastic loaded transversely), resolution of the equations, experimental verification of the results, use of finite element calculation software in order to reproduce the observed phenomena, - experimental study of the buckling of a compressed beam in different loading cases, use of finite element calculation software in order to reproduce the observed phenomena. The practical work associated with the "Finite Element Analysis" part aims to enable students to use calculation software recognized in the industry (ANSYS) by themselves, to make them discover the extent of the possibilities of this software and to make them aware of the risks of modeling errors. These TPs are: - discovery of the finite element method: principle of approximation and influence of the mesh - synthesis on the activity calculation of structures: dimensioning of a structure (comparison RDM -EF in the areas comparable to beams, study of influence of the mesh in the zones of stress concentrations, interpretation of the results, elastoplastic analysis .

Content

The course is divided into two parts.

A section "Strength of Materials" which exposes through courses and exercises, the physical parameters which influence the behavior of a structure.
This part contains the following chapters:
- calculations of displacements in beam structures,
- study of the particularities of hyperstatic structures compared to isostatic structures,
- introduction to plastic calculation, notions of plastic adaptation and plastic ruin,
- introduction to elastic instabilities and geometric nonlinearities, example of buckling of compressed beams.

A section " Finite Element analysis" which exposes through courses and comparisons of results of calculations, the parameters of analysis whose choices must be reasoned.
This part contains the following chapters:
- Finite Element method: notion of approximation and influence of the mesh,
- types of elements,
- boundary conditions
- analysis options.

Practical work is associated with each of these parts.

The practical work associated with the "Strength of Materials" part includes experimental verifications, in addition to finite element simulations. These pratical works are:
- equations of a nonlinear problem (flexible elastic loaded transversely), resolution of the equations, experimental verification of the results, use of finite element calculation software in order to reproduce the observed phenomena,
- experimental study of the buckling of a compressed beam in different loading cases, use of finite element calculation software in order to reproduce the observed phenomena.

The practical work associated with the "Finite Element Analysis" part aims to enable students to use calculation software recognized in the industry (ANSYS) by themselves, to make them discover the extent of the possibilities of this software and to make them aware of the risks of modeling errors. These TPs are:
- discovery of the finite element method: principle of approximation and influence of the mesh
- synthesis on the activity calculation of structures: dimensioning of a structure (comparison RDM -EF in the areas comparable to beams, study of influence of the mesh in the zones of stress concentrations, interpretation of the results, elastoplastic analysis .

Pre-requisites / co-requisites
EC Résistance des Matériaux et EC Mécanique du solide de l'UE Génie Matériaux et Structures

Bibliography
S. Viala, J.P. Noyel - Supports de cours mis à disposition sur l'Intranet ECAM. J.C. Craveur - « Modélisation des structures - calcul par éléments finis » 2ème édition Dunod D. Gay, J. Gamblin – « Dimensionnement des structures » hermes J.C. Craveur – P. Jetteur – « Introduction à la mécanique non linéaire » Dunod

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	Maximum duration: 2 hours Form: Exercises with answers in one box and MCQ.	2	Check understanding of the influence of physical parameters and analysis parameters on the results of a finite element analysis, depending on the modeling performed and the analysis conditions
2	Comparison of results of calculations of resistance of materials, and/or calculations by finite elements and for certain practical works, comparison with results of measurements.	1	Check the students' ability to use finite element software and to interpret differences between measurement results and calculation results