On singularities of the stress function at the corner points of the transverse cross-section of a twisted bar with a thin reinforcing layer

Abstract

The study of twisting of prismatic bars with a thin reinforcing layer is reduced, to the solution of the third boundary-value problem for Poisson's equation in the cross-sectional region of the bar /1/. However, the solution obtained by analytic or numerical methods does not always allow us to determine the singularities of the stresses near the corner points of the profile of the bar. The present article is devoted to a study of the asymptotic behavior of the solution of the third boundary-value problem for a Laplacian operator in a region with a corner point on the contour, and on this basis, the direct determination of the asymptotic properties of the stresses and coefficients of the stress intensity at the corner points of a transverse cross-section of a torsion bar with a thin reinforcing layer.