Further Deformations of the Axially-Symmetric Non-Bending Surfaces

Abstract

We consider a special class of symmetrically loaded thin shells of revolution, which in the presence of certain disturbances of the equilibrium deform without bending. The whole family of such surfaces can be regarded as complementary set to the four classes of equilibrium states of non-bending surfaces that we have studied in some depth recently. The new surfaces (with a few exceptions) have not a closed form description in elementary functions. Here we present their explicit parameterizations in terms of elliptic integrals.