An analytical method for piezoelectric composites containing doubly periodic piezoelectric fibers with ring-shaped cross-section under antiplane shear and its application

The piezoelectric composites containing a doubly periodic parallelogrammic array of piezoelectric fibers with ring-shaped cross-section are investigated under antiplane shear coupled with inplane electrical load. An analytical method is developed by using the generalized eigenstrain concept integrated with the doubly quasi-periodic Riemann boundary value problem theory. The generalized strains and stresses in each phase of the composites are obtained. As an example of application, the present solution is used to evaluate the effective electro-elastic coefficient of the piezoelectric composites with ring-shaped cross-section fibers. A comparison between the effective electro-elastic coefficient of the circular cross-section and ring-shaped cross-section piezoelectric fiber composites is carried out under the same piezoelectric fiber volume fraction, and much higher effective piezoelectric coefficients are observed for the ring-shaped cross-section piezoelectric fiber composites. Comparisons with the existing results and the results derived from the finite element analysis show the efficiency and accuracy of the present solution.