Determination of the Limit Equilibrium of a Piecewise-Homogeneous Cylindrical Shell with a Longitudinal Crack

Using the method of generalized problems of conjugation, for a piecewise homogeneous cylindrical shell with a longitudinal crack we develop a system of integral equations (some of which are singular) for functions of displacement jumps and their derivatives on the line of the crack and on the surfaces of separation of dissimilar component shells. The particular features of application of the method proposed to the case of a nonthrough crack are analyzed with due regard for plastic zones near its front and, also, for determining the redistribution of residual and temperature stresses, caused by the presence of a crack. The numerical analysis of the problem is performed, and certain relationships between the coefficients of intensity of efforts, moments, opening of the crack, and its size and distance to the surface of separation are established.