Refined small strain and moderate rotation theory of elastic anisotropic shells
A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to existing shell theories including the classical (i.e., linear Kirchhoff-Love) shell theory, Donnell-Mushtari-Vlasov shell theory, Leonard-Koiter-Sanders moderate rotations shell theory, von Karman type shear-deformation shell theory and moderate rotation shear deformation plate theory developed by J.N. Reddy. The present theory is developed from an assumed displacement field, nonlinear strain displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformation which should alter the bending, stability, and post-buckling behavior of certain shell structures as predicted using available theories.