Layer-wise finite-element analysis of a functionally graded hollow thick cylinder with a piezoelectric ring

In this work, a layer-wise finite-element formulation is developed for the analysis of a functionally graded material (FGM) hollow thick cylinder with one piezoactuator ring. The cylinder and ring is divided into many sublayers in the thickness direction and the full layer-wise shell theory is used to model a discretely stiffened FGM cylinder. In this model, the displacements are approximated linearly through each mathematical layer. This accounts for any discontinuities in the derivatives of the displacement at the interface of the ring and the cylindrical thick shell. This formulation is derived from the virtual work statement which includes the total structural potential energy and the electrical potential energy of the piezoelectric ring. Assembling stiffness and mass matrices, at each interface between two elements, stress and displacement continuity are forced, and then the finite-element model is solved. Static and dynamic responses of a functionally graded thick cylinder to electrical and mechanical loads with different exponent 'n' of FGM are determined to show the significant influence of the material in homogeneity. The results obtained at a distance far from the ring are compared with the mechanical behaviour of an FGM cylindrical shell without a ring. Because of the Saint Venant effects, the piezoelectrically induced deformation of the shell is confined to a region close to the piezoelectric ring; thus agreements between these two results are observed.