On the issue of a new solution of the materials resistance contact problem on compression of elastic cylinders in contact with parallel generators

Abstract

As a result of logarithmic singularity in the plane classical problem of elastically deformable material mechanics, it is proved that the reference formula for determining the convergence of two statically compressed parallel cylinders made of a homogeneous, isotropic, and physically linear material is not applicable. In the special case of elastic interaction of a cylinder with a half-plane, it is established that the convergence becomes equal to infinity. This paradoxical result confirms the inadequacy of Flaman’s model of a simple radial stress state in determining displacements. Based on this model, it is possible to determine only the stresses in parallel contacting cylinders, while the calculation of displacements, in this case, is not possible. Based on a previously developed and mathematically approximated by the authors flat design scheme of Flaman the algorithm exception of conflicts has been proposed. The algorithm is based on the integral Fredholm equation solution and can be seen as a new fundamental and applied elasticity theory problem, which is of great importance when assessing the contact of refined strength and stiffness of the cylindrical parts of the supporting structures subject to the general and local deformations (cylindrical rollers, gears, pavements with their seal steel rollers, etc.).