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The defining equations for a rigid/perfectly plastic shell are derived from basic principles. On the basis of a single geometric assumption for the velocity field, generalized strain rates and stresses are defined and equilibrium relations deduced. Shell yield conditions and flow law are discussed in general terms and then specifically for piecewise linear yield conditions. Preceding the general shell problem, the theory of beams under bending and axial forces is discussed to give a general insight into plastic structural behavior. The paper closes with an application to cylindrical shells and a discussion of areas for future development.
The defining equations for a rigid/perfectly plastic shell are derived from basic principles. On the basis of a single geometric assumption for the velocity field, generalized strain rates and stresses are defined and equilibrium relations deduced. Shell yield conditions and flow law are discussed in general terms and then specifically for piecewise linear yield conditions. Preceding the general shell problem, the theory of beams under bending and axial forces is discussed to give a general insight into plastic structural behavior. The paper closes with an application to cylindrical shells and a discussion of areas for future development.
The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed form solutions which can be useful for practical applications are derived for the case of a conical shell and a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure. The effect of the end conditions and the limitations of this approach are discussed in detail. (Author).
A nonlinear theory of large rotationally-symmetric plastic deformation of a sandwich-toroidal shell has been formulated. The generating curve for the toroid is assumed to be open and of an arbitrary shape. Deformation of the shell, described by the linear Cauchy's measure, is governed by the Love-Kirchhoff hypothesis. On the basis of the principle of virtual work non-linear equations of equilibrium have been derived. The material of the sandwich sheets is assumed to be rigid/perfectly-plastic and to obey the Levy-Mises theory of plastic flow and Huber-Mises-Hencky yield condition. The fundamental equations have been reduced to a system of six, coupled, ordinary, nonlinear differential equations which are, however, linear with respect to the first derivatives of unknown functions. By the use of a numerical procedure the initial/boundary problem can be reduced to a boundary value problem only, for each step of the loading process. Different types of boundary problems as well as continuity requirements have been discussed. (Author).