Bending of a long circular cylinder containing a thin spherical cap cavity

This paper deals with the three dimensional analysis of the stress distribution in a long circular cylinder containing a concentric very thin spherical cap cavity. The central plane of the cavity is perpendicular to the axis of the cylinder, and the cylinder is subjected to bending. The equations of the classical theory of elasticity are solved in terms of an unknown function which is then shown to be the solution of a Fredholm integral equation of the second kind. Numerical solution of the integral equation is obtained. The resultant stress intensity factors are presented in a graphical form for various proximity ratios.