Application of body force method to the analysis of stress concentration of an axi-symmetric body under bending. I. Basic theory and application to several simple problems (Q1062489)

A general theory is established for the application of the body force method to the stress concentration analysis of an axi-symmetrical body under bending. Determination of fundamental solutions in bending are not self-evident as in tension or torsion problems. However, comparing the boundary conditions to be satisfied along circumferential position of imaginary boundary and stress fields due to the body force distributed trigonometrically along a ring around the axis, it is found that three kinds of fundamental solutions are necessary and sufficient. Thus, the axi-symmetrical problem could be treated in the similar manner as two-dimensional problems. For example, problems of a spheroidal cavity and a troidal cavity in an infinite body under bending are solved numerically. The error in the former problem is less than 0.07 \%. The results of the latter problem agree with the exact solution in the two limiting cases; a deep hyperbolic notch and two dimensional elliptic hole.