On the problem of stress distribution in a rotating rod

Abstract

In our work "Distribution of stresses in rotating prismatic rods" the problem of determining the stresses in a rod rotating about an axis lying in the plane of the cross-section is solved. This question is reduced to solving two independent problems: the first of them does not depend on the shape of the cross-section contour and can be solved once; the second is reduced to considering a plane strain state. The general solution of the equations of elasticity theory was obtained after long and painstaking calculations by the method of E. Almanzi. We will show that this solution can be easily obtained using the general integral of the equations of elasticity theory in the Papkovich-Grodsky form.