Luo and Daniel [9] have shown that the macroscopic mechanical behavior of unidirectional fiber-reinforced brittle matrix composites can be correlated explicitly with the microscopic deformation and damage.Modeling and analysis of multilayer piezoelectric beams and plates have reached a relative maturity as attested by the numerous papers. Mindlin [10] presented the theory of piezoelectric crystals plate considering shear and bending. Chandrashekhara and Tiersten [11] developed general piezoelectric nonlinear theory and detailed the vibration equations of different piezoelectric crystals. Chandrashkhara, Tenneti [12] and Zhou et al. [13] investigated the dynamic control of laminated piezoelectric plates by the finite element (FE) method.

Wang and Rogers [14] presented a model for laminated plates with spatially distributed piezoelectric patches. Tzou and Gadre [15] analyzed thin laminates coupled with shell actuators for distributed vibration control. Xu et al. [16] analyzed the free vibration of laminated piezothermoelectric plate based on the 3D theory. Mitchell and Reddy [17] proposed the theory of the laminated piezoelectric plates by using classical plate theory and simple third-order theory, respectively. Noor and Peters [18] presented postbuckling analysis of multilayered composite plates subjected to combined axial and thermal loads and investigated the effects of mechanical and thermal loading on postbuckling behaviors of composite plates. Based on transverse shear-deformable theory, Librescu and Souza [19] gave the postbuckling analysis of geometrically imperfect flat panels under combined thermal and compressive edge loadings.

Shen Brefeldin_A [20] investigated the postbuckling behaviors of laminated plates with piezoelectric actuators under complex loading conditions based on Reddy’s higher order shear deformation plate theory. Oh et al. [21] studied thermal postbuckling behavior of laminated plates with top and/or bottom actuators subjected to thermal and electrical loads. In their analysis all the static/dynamic behaviors of laminated plates were investigated without considering the damage effects which would greatly influence the mechanical behaviors of smart structures. To the best of the author’s knowledge, up to now postbuckling analysis of piezoelectric structures considering the damage effects has rarely been investigated and reported. For example, Aydin [22] studied the dynamic characteristics of functionally graded beams with open edge cracks, in which an analytical method was proposed to determine the free vibration of beams with any number of cracks. Mao et al.