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This paper presents a nonlinear
high-order theory for cylindrical sandwich shells with flexible cores, extending a
previously presented high-order theory for sandwich plates. The outer and inner faces
are assumed to be relatively thin compared to the core and the effects from the core
compressibility are addressed in the solution by incorporating the extended nonlinear
core theory into the constitutive relations of the cylindrical shells. The governing
equations and boundary conditions for the cylindrical shells are derived using a
variational principle. Numerical results are presented for the cases where
the two faces and the core are made of orthotropic materials. These results
show that this model could capture the nonlinearity in the transverse stress
distribution in the core of the cylindrical sandwich shell. Numerical results
are presented on the details of the stress and displacement profiles for a
cylindrical sandwich shell under localized external pressure. This study could
have significance for the optimal design of advanced cylindrical sandwich
shells.