Buckling and vibration of multilayer orthotropic composite shells using a simple higher-order layerwise theory

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The buckling and vibration of thick, orthotropic laminated composite shells is modelled using a simple layerwise higher-order theory. The theory accounts for a cubic variation of both the in-plane displacements and the transverse shear stresses within each layer, the latter being zero at the free surfaces without the need for 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 FSDT, irrespective of the number of layers considered. A non-dimensionalized parameter called the General Performance Index is defined in order to assess the overall performance of the models based on their flexural frequencies and the largest component of stress within the laminate. Numerical results for moderately short, one-, two- and three-layer shell panels are obtained for a range of base layer-to-core modulus of elasticity ratios. The normalized natural frequencies and stresses of the present theory are compared with a simple layerwise first-order theory and two other global higher-order theories that despite their similarity, indicate some interesting differences. The critical buckling loads are also given for a range of modulus and thickness ratios. Results indicate the present theory generally performs better over a range of the parameters mentioned predicting conservatively lower natural frequencies, smaller buckling loads and larger stresses for symmetric shells.