Elastic-plastic problem for a perforated plate under transversal shear

Abstract

The problem of solving the problem of the transverse shear of a plate along the edges of the holes and weakened by a two-periodic system of rectilinear through cracks with plastic end zones, collinear to the abscissa and ordinate axes of unequal length, is considered. General representations of solutions are constructed that describe a class of problems with a doubly periodic distribution of moments outside circular holes and straight-line cracks with end zones of plastic deformations. Satisfying the boundary conditions, the solution of the problem of the plate shear theory 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.