ABSTRACT
The term shell is applied to bodies bounded by two curved surfaces, the distance between the surfaces being small in comparison with the other dimensions. The locus of points equidistant from these two surfaces defines the middle surface of the shell. The length intercepted between the two surfaces, along the normal to the middle surface at any point, defines its thickness. A shell is fully defined geometrically by specifying the form of the middle surface and the thickness of the shell at each point. Although the shell thickness may vary, it is assumed that the thickness remains constant, as is mostly the case in practice. The material of the shell is assumed to be isotropic, homogeneous and Hooke’s law is valid although nonisotropic cases are considered in this chapter. However, the basic assumption in the linear theory of shells that the displacements of the shell are considered to be small in comparison to the thickness is abandoned in the present nonlinear analysis of shells. Two different classes of shells can be identified, namely thick shells and thin shells. A shell is called thin if the maximum value of the ratio h/R, where h is the thickness of the shell and R is the principal radius of curvature of the middle surface, can be neglected in comparison to unity. Whenever this ratio is large in comparison to unity so that it cannot be neglected, then the shell is classified as a thick shell. This classification is not fully defined unless a definite value of this ratio is specified below which this ratio can be neglected. A thin shell may be defined as the one that corresponds to a ratio of h/R less than or equal to 1/20. If the ratio is beyond this range, then the shell is regarded as thick and the formulation of these classes of problems are much more complicated than those of thin shells. It should be noted, however, that in a large number of practical applications the ratio of h/R lies in the range between 1/50 and 1/1000, making the theory of thin shells of great practical importance. It follows from the above discussion that shells retain the same relation to plates as curved beams to straight beams and therefore shells are often referred to as curved plates in the literature. Thus it is clear that there is an anology between plates and shells, suggesting an alternate name of curved plates to define certain types of shells. This analogy is the basis for the usefulness of a number of methods used in the analysis of the theory of thin plates.
