An alternative formulation in linear bifurcation analysis of laminated shells

Most of the previous research on buckling and stability of shell structures is confined to u–v–w or w–F formulation, which are limited either by accuracy or by the chosen kinematic theory. In this work, an alternative mixed formulation is proposed for general laminated shells of revolution and calculated for different shell theories. Its principle consists in choosing the set of unknown functions as the obtainable boundary conditions from the variational formulation.The main advantage of the mixed formulation is direct involvement of the stiffness matrices, without their derivatives. This quality is most important in complicated woven-fabric procedures when the derivative functions of the fiber orientations are not available or the constitutive functions have discontinuities.The proposed formulation is validated and demonstrated for filament-wound laminated conical shells with variable material properties.