ASYMPTOTIC ANALYSIS OF THE EVERSION OF NONLINEARLY ELASTIC SHELLS

In this paper we study the eversion of axisymmetric, strictly convex, nonlinearly elastic shells within a general, geometrically exact theor y in which the shell can suffer flexure, extension, and shear. Each su ch theory is endowed with a thickness parameter epsilon(2). For such s hells with free or with fixed hinged edges, we give conditions on epsi lon and the data ensuring that there is an everted state under zero ap plied load, we show how to approximate it effectively with an asymptot ic series in epsilon whose error we can estimate, we determine the qua litative properties of the everted state, paying particular attention to the formation of a lip near the edge, and we give specific formulas for the shape, the strains, and the stress resultants.