Formation of Discontinuities in Rectangular Plates as a Result of Residual Stress Relief

Abstract

The paper deals with the problem of relieving residual stresses in an elastic domain of rectangular shape with free sides as a result of the formation of a discontinuity of particular shape. First, we construct the solution to the problem of residual stresses in an infinite strip with free sides and with a central transverse cut on which a discontinuity of displacements is known. Then, the solution for a rectangle is added to this solution, with the help of which the boundary conditions at the ends are satisfied. The formulas for the residual stresses and for the corresponding displacements are represented in the form of series in Papkovich-Fadle eigenfunctions. The expansion coefficients (Lagrange coefficients) have the form of simple Fourier integrals.