Based on the concept of an “intermediate” class of deformations, a theory suitable for the nonlinear static and dynamic analysis of transverse shear deformable circular and noncircular cylindrical shells, composed of an arbitrary number of linearly elastic monoclinic layers, is developed. The theory is capable of satisfying zero shear traction boundary conditions at the inner and outer shell surfaces. Upon assuming that the shell is subjected to a certain initial stress state and applying the highly nonlinear governing equations derived to the adjacent equilibrium criterion, a set of Love-type linearized equations is further derived. These latter equations are suitable for buckling and/or vibration analyses; in a companion paper, they are solved and used for the study of the influence of transverse shear deformation on the buckling loads of axially compressed cross-ply laminated circular and oval cylindrical shells.

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