A MODIFIED METHOD OF ELASTIC SOLUTIONS AND ESTIMATION OF ITS EFFICIENCY IN PROBLEMS OF PLASTICITY FOR SHELLS OF REVOLUTION

The calculation of the elasioplastic stress-strain state (SSS) for shells of revolution, the stiffness of which varies in two directions [1, 2], is a complex problem which requires a considerable computational effort. For this class of problems, the method of variable parameters of elasticity [4] or the method of elastic solutions [5] are commonly used. It is known that the method of variable parameters of elasticity converges more rapidly [6, 7]. However, the method of elastic solutions involves seeking the general solution of the homogeneous system of resolving equations only for a first approximation. Forall subsequent approximations, all one need to do is to construct only a partial solution of the nonhomogeneous system. Moreover, for shells the thickness of which is independent of the circumferential variable the resolving system splits into a scries of independent subsystems. For this reason, we consider a modified method of elastic solutions which demonstrates an accelerated convergence in comparison with that of the method of elastic solutions. We also consider an efficient method of solving the problem of plasticity for shells of revolution the sliffness of which varies in two directions. This method is based on the modified method of elastic solutions.