Numerical Research Of Singularities In Piezoelectric Wedges And Junctions

Interfaces are important microstructures of piezoelectric composites. Many interface wedge and corner cracks exist in the structures of piezoelectric composites, and these usually become the initial damage points. As a result of the singular stress field and the singular electric displacement field near the interface wedges and the interface corners, the parameters such as the order of stress singularity and the order of electric displacement singularity, the angle function of stress and electric displacement must be resolved, in order to find reliable evaluative method which apply to piezoelectric composites.An eigenvalue method was proposed to study the singular stress field and the singular electric displacement field under the plane problems of piezoelectric interface wedge and comer. The major work of this paper is as follows:1. Based on the fundamental equations of the transversely isotropic piezoelectric materials under the Cartesian coordinates, by using of the coordinate transformation, we get the fundamental equations under the Polar coordinates. Based on the first-order approximation assumption of the piezoelectric materials, the discrete characteristic equation was derived by using the displacement functions and electric potential functions with separated variables and the meshless method. The eigenvalue is relative to the order of stress singularity and electric displacement singularity, and the associated eigenvector is with respect to the stress angular variations and electric displacement angular variations. The order of stress singularity and electric displacement singularity, and the associated stress and displacement angular variations was obtained. 2. With the different working conditions, such as the wedge angle, type of material, boundary condition and the polar of piezoelectric, the influence of stress singularity and electric displacement singularity, and the associated normalized stress and displacement angular variations were discussed. By comparing with the known numerical results, we can verify the accuracy and efficiency of the method.