A local high-order deformable theory for the bending analysis of thick laminated cylindrical shells is developed here. The shell displacements in this theory are assumed to be high-order polynomial functions layer-by-layer through the shell thickness. The displacement continuity constraints at the interface between layers are introduced into the potential energy functional by the Lagrange multiplier method. A set of governing equations and admissible boundary conditions based on this modified potential energy functional are derived. The present analytical solutions of cross-ply circular cylindrical shells with shear diaphragm supports are determined by using the Fourier series expansion method. The present analytical solutions are compared with the 3-D elasticity solutions and the analytical solutions obtained from other laminated cylindrical shell theories. This reveals that the present results agree very closely with the 3-D elasticity solutions.
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