Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses

The Mehler–Fock transformation method is used to study the rolling of a rigid cylinder over a half-plane with initial stresses. The problem is reduced to a system of two dual integral equations, which are then reduced to a system of two integral Fredholm equations of the second kind. The system of integral equations is solved by the method of degenerate kernels. The dependences of the normal and tangential stresses on the elongation are plotted.     

Rolling of a Rigid Cylinder Over a Strip with Initial Stresses

An asymmetric quasistationary problem for a strip with initial stresses is formulated and solved. Resolving differential equations are derived and then reduced to five functional equations by the Hankel integral transform. Two of these equations are reduced to the Fredholm integral equations of the second kind, which are solved by the method of degenerated kernels. The normal and tangential stresses are plotted versus the elongation.