The theorems of limit analysis are applicable to an approximate theory if, and only if, the approximate equilibrium and strain-rate-velocity relations are such that the principle of virtual work holds between them. A theory for which this is true may be called “consistent.” Such a consistent theory is developed for shallow shells of revolution, and the methods of limit analysis are applied to particular cases of shallow parabolic and conical shells under normal and axial loads. Bounds are obtained on the plastic interaction curves using the two-moment, limited-interaction yield curve.

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