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The known solution for the plastic instability failure of an infinite cylell unerinternal pressure is extended to shells of finite length. An incremenl of plasticity is used in the analysis, in conjunction with Trescandio. IT I CONSIDERED THAT THE SHELL IS MADE OF A RIGID PLASTIC MATERIA WHICH XHIBITS STRAIN HARDENING AND OBEYS Ludwik's power law. The ends of the shell are constrained in such a manner as to prevent radial motion but to permit axial displacements. Membrane theory is used throughout, and restraining moments are considered negligible in the plastic range. Conditions for instability are investigated at the shell's equator. In the analysis, a deformed contour in the shaabola is assumed for the shell's meridian. However, the solution at the equator does not appear to be particularly sensitive to changes in meridian contour. As expectd, higher pressures can be obtained in the finite shell, before the onset of instability, than in the infinite shell. (Author).
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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.
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