Metody Wariacyjne w Teorii Sztywno-Plastycznych Powłok Cylindrycznych

The problem of the transition of shells into the plastic state for cylindrical bending is one of the more straightforward problems in the theory of rigid-plastic shells.
In this paper, the problem has been formulated and solved on the basis of variational methods worked out previously by the authors (1-5). It is shown (Sec. 1) that in the general three-dimentional formulation of the problem for arbitrary rigid-plastic media, the limiting Joad is determined by the perfectly plastic part of the function of dissipation of the medium.
Subsequently it is shown (Sec. 2-5) that the classical theory of (perfect) shells based on the assumption of disregarding the shear strain in the material of the shell constitutes an asymptotically exact theory of the problems of stretching and bending at a shell thickness approaching zero.
Evaluations are presented of deviations of the asymptotic values of limiting loads obtained at a low thickness of the shell from the limiting loads for perfect shells obtained during simultaneous stretching and bending.
It appears that all the results are valid also in the case of curvilinear shells. General formulae are presented (Sec. 6-8) for the determination of limiting loads both for problems statically determined and for those statically indetermined.
Evaluations are indicated of deviation of the limiting loads for shells With finite thickness from the limiting Ioads for a perfect shell, and where the relation is shown between these estimations and the character of the distribution of loads (Sec. 9).
Consideration is given to the qualitative properties of the destructive field of velocity (i.e., a velocity field corresponding to the Jimiting load) with the assumption that these fields satisfy the Kirchoff hypothesis (Sec. 10). In particular, the problem of the formation of a neck during destruc­tion is considered, together with the analogy of Saint Venant's principle.