Shell theory and its specialized branche

For small-strain unrestricted deformation of thin elastic shells the ®eld equations and variational principles are rederived in terms of variables immediately representing physical quantities. The relevant strain and stress tensors turn out to be identical to those commonly known as the `modi®edʹ and the `bestʹ. The nonlinear theory exhibits a static-geometric duality. For orthogonal coordinates the tensor-form theory leads to a modi®cation of the Lure± Novozhilov formulation. The general theory is specialized to that of `quasi-shallow shellsʹ, to the membrane theory and to ¯exible-shell theory, which are explored with respect to basic hypotheses and accuracy. #