SHALLOW THIN ELASTIC SHELLS - CONTINUOUS TRANSITION BETWEEN PLATE ANDSHELL THEORIES

We consider in the framework of linear elasticity a family of shells o f thickness 2epsilon, depending on the parameter delta: the medium sur face is x3 = deltapsi(x1, x2). For delta = O(epsilon) the problem reli es on plate theory (or ''shallow shells'') whereas for delta = O(1) is a shell problem, which may be, according to the shape and to the boun dary conditions, with inhibited or not-inhibited pure flexions. In bot h cases we prove that, for delta large with respect to epsilon but sma ll with respect to 1, the asymptotic forms of plate theory for large l ambda = delta/epsilon and of shells for small delta coincide.