Structural Analysis

General Data
Academic program	General Engineering Program			:
Type d'EC	Classes (LIIAem06ECalStr)
Lectures : 20h00 Lab Work : 16h00 Total duration : 64h00	Status :	Period : SEMESTER 6	Education language : French

Learning Outcomes
- calculate displacements in the case of a structure of beams - calculate the reactions of the connections of a hyperstatic structure -use finite element software to obtain stress strain and displacement values: choose the type of elements appropriate to the problem; evaluate the quality of a mesh; determine the need for non-linear analysis (geometry or material); choose the criterion to be used depending on the material used (e.g. ductile or brittle) - Solve elastoplastic problems in the case of systems composed of bars.

Learning Outcomes

- calculate displacements in the case of a structure of beams
- calculate the reactions of the connections of a hyperstatic structure
-use finite element software to obtain stress strain and displacement values: choose the type of elements appropriate to the problem; evaluate the quality of a mesh; determine the need for non-linear analysis (geometry or material); choose the criterion to be used depending on the material used (e.g. ductile or brittle)
- Solve elastoplastic problems in the case of systems composed of bars.

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 "Finite Element analysis" section which explains, through lectures and comparisons of simulation results, the analysis parameters whose choices must be reasoned. This part contains the following chapters - Finite Element Method - theoretical approach: notion of approximation and influence of the mesh, - Finite Element Method - practical aspect: types of elements, boundary conditions, analysis options. - geometrical non-linearity material non-linearity: elastoplastic calculation 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 "Finite Element analysis" section which explains, through lectures and comparisons of simulation results, the analysis parameters whose choices must be reasoned.
This part contains the following chapters
- Finite Element Method - theoretical approach: notion of approximation and influence of the mesh,
- Finite Element Method - practical aspect: types of elements, boundary conditions, analysis options.
- geometrical non-linearity
material non-linearity: elastoplastic calculation

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 and EC Mécanique du solide from UE Génie Matériaux et Structures

Bibliography
S. Viala, J.P. Noyel -documents on moodle 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	All the learning outcomes except the practical use of software
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	use finite element software to obtain stress and displacement values: choose the type of elements appropriate to the problem; evaluate the quality of a mesh; determine the need for non-linear analysis (geometry or material); choose the criterion to be used depending on the material used (e.g. ductile or brittle)