(i) The general theory of elastic shells is based on the following three assumptions: (a) The...

(i) The general theory of elastic shells is
based on the following three assumptions: (a) The displacement vector is linear
and normal to the coordinate curves in the middle surface. (b) The distances
between points on a normal to the undeformed middle surface do not change
during deformation. (c) The stresses are replaced by a system of stress and
moment resultants. Show that moment and stress and moment resultants for
shallow spherical shell satisfy the relationships