Free vibration analysis of FGM shell structures with a discrete double directors shell element

Free vibration response of functionally graded material (FGM) shell structures is studied by using an efficient 3d-shell model based on a discrete double directors shell element. With this element, the vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. The mechanical properties of the shell structure are assumed to vary continuously in the thickness direction according to the general four-parameter power-law distribution in terms of the volume fractions of the constituents. The fundamental equations for the FGM shell structures are derived using principle of virtual work. Performance and accuracy of the present discrete double directors shell model (DDDSM) are confirmed by comparing the present solutions obtained from finite element analyses with the existing results in the literature.