On singularities in the solution of a problem for an elastic half-plane with a rod emerging orthogonally on the boundary
An integro-differential equation in the contact stress is investigated for for an elastic half-plane (isotropic and orthotropic) with an extensible rod emerging orthogonally on the boundary. The question of the nature of the contact stress singularity at the point where the rod emerges at the boundary is clarified. It is shown that the asymptotic form of the Cauchy-type integral does not enable a single-valued solution of the question of the nature of the singularity to be obtained if it is assumed to be power-law logarithmic. The true nature of the singularity is determined by an exact solution of the equation constructed using the Mellin integral transform and the Carleman boundary value problem for a strip.
asymptotic form of the Cauchy-type integral
scientific article; zbMATH DE number 3940979