TABLE OF CONTENTS The problem of axisymmetric shells is of sufficient practical importance to include in this chapter special methods dealing with their solution. While the general method described in the previous chapter is obviously applicable here, it will be found that considerable simplification can be achieved if account is taken of axial symmetry of the structure. In particular, if both the shell and the loading are axisymmetric it will be found that the elements become 'one dimensional'. This is the simplest type of element, to which little attention was given in earlier chapters.
The first approach to the finite element solution of axisymmetric shells was presented by Grafton and Strome.1 In this, the elements are simple conical frustra and a direct approach via displacement functions is used. Refinements in the derivation of the element stiffness are presented in Popov et al.2 and in Jones and Strome.3 An extension to the case of unsymmetrical loads, which was suggested in Grafton and Strome, is elaborated in Percy et al.4 and others.5 ,6
Later, much work was accomplished to extend the process to curved elements and indeed to refine the approximations involved. The literature on the subject is considerable, no doubt promoted by the interest in aerospace structures, and a complete bibliography is here impractical. References 7 15 show how curvilinear coordinates of various kinds can be introduced to the analysis, and references 9 and 14 discuss the use of additional nodeless degrees of freedom in improving accuracy. 'Mixed' formulations have...
