Bending and free vibration of multilayered functionally graded doubly curved shells by an improved layerwise theory

An improved layerwise theory is established for the bending and vibration responses of multi-layered functionally graded doubly curved shells with material properties varying gradually and continuously across the whole shell thickness. The theory accounts for shear deformation and normal strain effects by assuming for each layer, a displacement field with zigzag first-order in-plane displacements and through-the-thickness parabolic transverse displacement. Moreover, it is assumed a stress field satisfying the loading conditions on the external shell faces and the continuity conditions of the internal stresses at the layers interfaces, so, there is no need for introducing in the present formulation any shear correction factor. For this purpose, a mixed variational statement is used. The continuity conditions for the displacements at the layers interfaces are used to decrease the degrees of freedom of the theory. Bending and free vibration problems are solved for FGM single- and three-layered sandwich open cylindrical and spherical shells with completely simply supported or clamped edges. Comparisons for some present results with numerical results obtained by other authors due to advanced 2D and 3D elasticity solutions are made showing the high efficiency of the present theory in predicting the bending and vibration parameters. Graphics are presented to demonstrate the importance of the normal strain effect for the static bending and free vibration of the considered shells.