An improved zig-zag model for the bending of laminated composite shells

A simple layerwise higher-order zig-zag model is proposed for the bending of laminated composite shells. The model provides a cubic variation of both the in-plane displacements and the transverse shear stresses within each layer. As the displacement model satisfies the zero transverse shear stress conditions at the free surfaces, there is no need for the use of shear correction factors. By imposing the continuity of the in-plane displacements and the transverse shear stresses at the interfaces, the number of variables is shown to be the same as that given by the first-order shear deformation shell theory, irrespective of the number of layers considered. For the sake of consistency, all terms of the order of the thickness coordinate-to-radius ratio have been retained in the derivation of the governing equations. Numerical results for the cylindrical bending of thick, symmetric homogeneous orthotropic and three-layer laminated shells under sinusoidal loading show that the maximum transverse deflections and in-plane stresses are in good agreement with available exact elasticity solutions for radius-to-thickness ratios greater than or equal to four.