Anti-plane problem for a piezoelectric fiber embedded in a functional graded piezoelectric matrix

Based on the complex variable method and Stroh formalism, this paper studied the stress and electric displacement field distribution of a functional graded piezoelectric matrix with a piezoelectric fiber. According to the continuous conditions between the piezoelectric matrix and the fiber and using the method of piece-wise homogeneous layers, the stress and electric displacement field of any functional graded piezoelectric matrix are derived. And the stress and electric displacement field of any functional graded piezoelectric matrix properties are analyzed. It is shown that the stress and electric displacement field are greatly affected by the property of matrix and variation of material constants of the matrix property.