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# Cours scientifique - PHY304 : Solid Mechanics

## Descriptif

Prerequisites: PHY101, PHY102, PHY105, PHY201, PHY206. Some knowledge of ordinary differential equations would be helpful.

We are surrounded by natural and man-made structures that deform when subjected to loadings. These structures span a wide spectrum of length scales, from suspension bridges and aircrafts all the way down to spider webs, human hair, micro-electro-mechanical systems, and cell membranes. In this course, we will focus on slender bodies, which by virtue of their elongated aspect can be modeled as curvilinear media. This simplified geometry permits the introduction of the fundamental concepts of the mechanics of deformable solids without recourse to the heavy mathematical formalism that is inherent to the description of their three-dimensional counterparts. It will thus allow us to solve problems and comprehend phenomena (such as the buckling of elastic beams) involving geometric or behavioral nonlinearities that, in three dimensions, do not lend themselves to analytical treatment.

We will cover the following topics:

• Geometry, deformation, and kinematics of curvilinear media
• External and internal forces and couples, equilibrium equations
• Constitutive relations, including rigid bars, extensible strings, and elastic rods
• Boundary value problems associated with various models: elastic strings, beams, and arcs
• Euler's elastica (and, time permitting, its boundary layer)
• Linearized elasticity of slender bodies and its applications
• Stability of conservative systems (first discrete systems, later, via the calculus of variations, continuous systems)

and, time permitting,

Dynamics: wave propagation in elastic beams, forced and free vibrations of elastic rods

## Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vous devez avoir validé l'équation suivante : UE PHY101 Et UE PHY102 Et UE PHY105

Numérique sur 20

## Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)
L'UE est acquise si Note finale >= 9
• Crédits ECTS acquis : 5 ECTS

La note obtenue rentre dans le calcul de votre GPA.

## Pour les étudiants du diplôme M1 - Mechanics

Le rattrapage est autorisé (Note de rattrapage conservée)
L'UE est acquise si note finale transposée >= C
• Crédits ECTS acquis : 3 ECTS

La note obtenue rentre dans le calcul de votre GPA.

## Pour les étudiants du diplôme Echanges PEI

Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)
L'UE est acquise si note finale transposée >= D
• Crédits ECTS acquis : 5 ECTS

La note obtenue rentre dans le calcul de votre GPA.