Stresses in an Elastic Circular Cylinder with a Spherical Cavity under Transverse Bending

抄録

This paper contains a three-dimensional solution for the stresses and deformations arising in an elastic circular cylinder with a spherical cavity under transverse bending. The method used here is based on Dougall's stress function approach referred to the cylindrical and spherical coordinates. The problem can be reduced to one of two simply connected domains, i. e., an infinite circular cylindrical region and an infinite region excluding a spherical cavity. The two stress functions in each region are given by simple expressions of the cylindrical and spherical harmonics. The boundary conditions on the surface of the cylinder and of the spherical cavity are satisfied by using the relations between the cylindrical and spherical functions. Numerical results are given for five different radii of the cavity.