Finite-element analysis

The walls, covers and bases of circular tanks and silos frequently have the shape of axisymmetrical shells of revolution. Any of the structures shown in Figures 1.1 or 5.1(a) can be idealized as an assemblage of conical shell elements and analysed by the finite-element method. A typical conical shell element, which is relatively simple, but known to give accurate results (Figure 5.1b), will be presented in this chapter. The thickness of the shell within each element is constant, but can vary from element to element. For accuracy, small elements should be used, particularly where the stress varies rapidly. (Element length in such a zone may be chosen equal to π/(20β), where β is defined by equation (2.13).) The material of the shell is assumed elastic isotropic; the thickness of the shell is considered small with respect to the radius, such that shear deformation can be ignored. Only the case of axisymmetrical loading is considered here. Because of its frequent practical occurrence, the finite-element analysis of shells of revolution has been treated by many authors1, offering refinement to improve accuracy and reduce the number of finite elements required in the idealization. However, the relatively simple element presented in this chapter is adequate for practical design.