Solution of the problem of the elasto-plastic deformation of a shell structure

An analytical solution of the boundary problem, which is one of the different forms of the approximate method of elastic solutions, is obtained within the framework of the deformation theory of small elastoplastic strains for the Kirchoff-Love model of a shell structure loaded by constant pressure. Completely stable approximations of partial solutions of the differential equations resolving the problem of the deformation of a cylindrical shell with compulsorily assigned initial strains are plotted using specially selected basis and weighting functions, and also boundary conditions formulated for the elasto-plastic section. In an example of an annular vessel, the permissible shaping of which is restricted by safety concerns, the variation in the width of the gap between cylindrical shells is analyzed elasto-plastically.