Exact solutions are derived of the classical differential equations defining the deformations of axially compressed thin-walled circular cylindrical shells. The end conditions along the circular edges are assumed as the vanishing (a) of the radial displacement; (b) of the longitudinal bending moment; (c) of the variation in the axial normal stress resultant; and (d) of the circumferential membrane shear stress resultant. Under these conditions of simple support the critical value of the uniformly distributed axial normal stress is one half the classical critical value.

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