Chapter 9 - Spherical Shells

Abstract

Spherical shells are another special case of shells of revolution. For these shells, a circular arc, rather than a straight line, revolves about an axis to generate the surface. If the circular arc is half a circle and the axis of rotation is the circle's own diameter, a closed sphere will result. The equation of spherical shells can be obtained by deriving and substituting the proper Lamé parameters of such shells in the general shell equations. The equations for the general thin shells are applicable for spherical shells with the appropriate change in the coordinate system to that of the spherical shells. The orthotropy of the material treated here is spherical orthotropy. Similar to conical shells, the assumption is made that the stiffness parameters are constant. The free vibrations of spherical shells can be tackled by different methods and researchers have used finite elements to solve the vibrations of spherical shells.