These lectures cover the non-linear mechanics of thin and slender structures. The goal of the lectures is to understand the rich mechanical behavior of structures through the analysis of one-dimensional models (such as the elastic rod model, the inextensible thread model) or two-dimensional models (such as the elastic plate model). These behaviors are illustrated by applications ranging from civil engineering to biology.
In the first part, we derive the elastic rod model starting from the equations for a three-dimensional elastic solid: we introduce methods for dimensional reduction and identify the conditions where the 1D models are applicable (depending on the load intensity, on the elastic stiffness of the body and its geometry).
In the second part, we apply these 1D models, starting with the framework of the "strength of materials" familiar to engineers (linear elasticity). The nonlinear response is covered in detail with a particular emphasis on geometrical nonlinearity and instabilities (buckling, snap-through). Material nonlinearity is also discussed with the example of necking.
In part three, we show how the tools introduced for the analysis of 1D structures can be extended to the analysis of thin shells and thin plates (2D bodies).
This class will include a detailed discussion of real-world examples and applications (tentatively 30 min each week). It includes an in-depth review of fundamental notions in continuum mechanics such as variational principles, kinematical constraints, dynamics and vibrations, constitutive laws, stability and material or geometrical nonlinearity, and simulation methods. All these notions are treated in a simple 1D framework. This class builds up on the fundamental notions introduced in MEC430 but is at a more advanced level. The material introduced in MEC430 will be shortly reviewed; new material introduced in this class includes material nonlinearity, viscous constitutive laws, a general discussion of stability.
Prerequisite : MEC 430 : Mécanique des Milieux Continus I
Language : English or French, on demand (Petites Classes in French)
Credits ECTS : 4
Dernière mise à jour : 23 mars 2016