The Finite Deformation of a Hollow Sphere subjected to Internal or External Pressure

Abstract

This paper is concerned with the deformation of a hollow sphere, within the theory of finite elastostatics for a particular homogeneous isotropic commpressible material, the so-called Blatz-Ko material. The body is subjected to uniform pressure, either internal or external. In the case of internal pressure, it is found that there is a maximum pressure beyond which there does not exist a solution. Under that pressure there exist two sets of solutions. In the case of external pressure, the location of the maximum value of the compressive hoop stress departs from the inner surface. There exists, howeverc a supremum of the location. If the hollow sphere is thinner than the supremum, the maximum value of the compressive hoop stress occurs at the outer surface.