Geometric Formalism of Shell Theory

Shells are classically described geometrically by a middle surface (a two dimensional surface embedded in ℝ3) and a thickness which is generally constant. In this book, we will focus on thin shells whose thickness is small with respect to the characteristic dimension of the middle surface. Moreover, we will restrain our analysis to the linear elastic framework. Thus in this book, the thin elastic shells studied will be described by Koiter shell model, or at the limit by the membrane model, which are two-dimensional models involving only the variables of the middle surface.