TABLE OF CONTENTS A shell is, in essence, a structure that can be derived from a plate by initially forming the middle surface as a singly (or doubly) curved surface. The same assumptions as used in thin plates regarding the transverse distribution of strains and stresses are again valid. However, the way in which the shell supports external loads is quite different from that of a flat plate. The stress resultants acting on the middle surface of the shell now have both tangential and normal components which carry a major part of the load, a fact that explains the economy of shells as load-carrying structures and their well-deserved popularity.
The derivation of detailed governing equations for a curved shell problem presents many difficulties and, in fact, leads to many alternative formulations, each depending on the approximations introduced. For details of classical shell treatment the reader is referred to standard texts on the subject, for example the well-known treatise by Fl gge1 or the classical book by Timoshenko and Woinowski-Krieger.2
In the finite element treatment of shell problems to be described in this chapter the difficulties referred to above are eliminated, at the expense of introducing a further approximation. This approximation is of a physical, rather than mathematical, nature. In this it is assumed that the behaviour of a continuously curved surface can be adequately represented by the behaviour of a surface built up of small flat elements. Intuitively, as the size of the subdivision decreases it would seem that convergence must occur...
