Descriptif

We are surrounded by natural and man-made structures that deform when subjected to various loadings. These structures span a wide spectrum of length scales, from suspension bridges and aircrafts all the way down to spider webs, human hair, microelectromechanical 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 allows us to present the fundamental concepts of the mechanics of deformable solids without recourse to
the tensor formalism that is intrinsic to three-dimensional continuum mechanics. We will then solve problems and comprehend phenomena (such as the buckling of elastic beams) involving geometric and/or material nonlinearities that, in three dimensions, do not lend themselves to analytical treatment.

We will cover the following topics:
 
o Geometry, deformation, and kinematics of curvilinear media;
o External and internal forces and moments, equilibrium equations;
o Constitutive relations, including rigid bars, extensible strings, and elastic rods;
o Boundary-value problems associated with various models: elastic strings, beams, and arcs;
o Euler’s elastica;
o Linear elasticity of slender bodies (strength of materials);
o Stability of conservative systems, both discrete and continuous;
o Dynamics: wave propagation in elastic beams, and forced and free vibrations of elastic rods.