The Theory of Rotationally Symmetric Plastic Shells

Abstract

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 the 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 Mises yield condition for rotationally symmetric shells

“…(2.8a) or (2.8b). The dividing "hypercurve" between them may be found directly by setting sin y = 0 before integrating the generalized stresses [10] Much simpler expressions are obtained for an ideal sandwich shell composed of two thin sheets of thickness J each, separated by a core of thickness 2H'. The sheets are so thin that the stress variation across each sheet can be neglected; the core has no tensile strength but can carry the necessary shear.…”

Untitled

“…(2.8a) or (2.8b). The dividing "hypercurve" between them may be found directly by setting sin y = 0 before integrating the generalized stresses [10] The corresponding strain rates are…”