Mathematics

A longstanding problem in the mathematical theory of elasticity is to predict theories of lower-dimensional objects (such as rods, plates or shells), subject to mechanical deformations, starting from the 3d nonlinear theory. For plates, a recent effort has lead to rigorous justification of a hierarchy of such theories (membrane, Kirchhoff, von Karman). For shells, despite extensive use of their ad-hoc generalizations present in the engineering applications, much less is known from the mathematical point of view. In this talk, I will discuss the limiting behavior (using the notion of Gamma-limit) of the 3d nonlinear elasticity for thin elliptic shells, as their thickness h converges to 0, under the assumption that the elastic energy of deformations scales like h^\beta, with 2 Seminars -