Invariant Multicouple Theory of Shells

The multicouple theory is applicable to finite deformations of thick elastic or inelastic shells. A hierarchy of two-dimensional stress and strain measures is established and a systematic procedure is given for establishing a theory of any order. The one-couple theory is an extension of the first approximation theory of Love and includes an effect of transverse shears. When the Kirchhoff hypothesis is invoked, the one-couple theory reduces to the usual first-approximation. A higher-order theory gives a better description of the distributions of stress and strain in terms of two-dimensional variables, multistresses and multistrains. Each successive m-couple theory provides a progressive relaxation of the first approximation and consistent refinements of stress distributions within the shell, upon the surfaces and edges. Consequently such theories offer new approaches to problems of inelastic behavior and a means to study thick shells, particularly, the behavior at the junctures of different elements.