Vibration and stability of simply supported cross-ply doubly curved shells

A discrete-layer, higher-order theory for the vibration and stability analyses of the thick, doubly curved laminated shell is presented. The theory accounts for the effects of transverse shear and normal deformations. The displacements of the shell in the theory are assumed to be layer-by-layer higher-order polynomial functions through thickness of the shell. The displacement continuity conditions at the interface between contiguous layers are imposed as the constraints and are introduced into Lagrangian functional of the shell. A set of the motion equations is obtained by applying the generalized variational principle to the modified Lagrangian functional of the shell. The present analytical solutions for the natural frequencies and buckling loads of cross-ply laminated shells with fully simple supports are obtained by using the Fourier series expansion method. They are then compared with the three dimensional elasticity solutions and the analytical solutions obtained from other laminated shell theories. The effects of aspect, curvature radius to side, and elastic modulus to shear modulus ratios on the natural frequencies and buckling loads are studied. The modal transverse shear and normal stresses are also evaluated.