ELASTOPLASTIC PROBLEM FOR PERFORATED PLATE IN TRANSVERSE SHEAR

Abstract

A solution is given to the problem of transverse shear of a thin plate clamped along the edges of the holes and weakened by a doubly periodic system of rectilinear through cracks with plastic end zones collinear to the abscissa and ordinate axes of unequal length. General representations of solutions are constructed that describe the class of problems with a doubly periodic stress distribution outside circular holes and rectilinear cracks with end zones of plastic deformations. Satisfying the boundary conditions, the solution of the problem of the theory of shear plates is reduced to two infinite systems of algebraic equations and two singular integral equations. Then each singular integral equation is reduced to a finite system of linear algebraic equations. Keywords: perforated thin plate, straight cracks with end zones, transverse bending, plastic deformation zones.