13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- (a) [0 / 90 ]s o o (b) [90 / 0 ] s o o Figure 5. Distributions of electric field strength components iE On the basis of comparative analyses in this section, it is seen that the results of Artel and Becker [13], and Mirzababaee and Tahani [14] violate traction free boundary conditions at free edges. Furthermore, the FEM solution from Artel and Becker [13] fails to guarantee the continuity of transverse normal stress at interface of two different materials, deficiencies mentioned above were overcome by present solution. Both the stress and electric field strength singularities were observed with suitable layer refinement in z-direction. 4. Conclusions State space method for an analytical solution has been developed to investigate the coupling effect on piezoelectric laminated plates and the singularities in the vicinity of free edges. Cross-ply laminated plates with and without electromechanical coupling subjected to uniform axial strain have been studied. To validate this method, comparisons were made between present results and those of other analytical and FEM solutions in the literature. By satisfying all the mechanical and electric boundary conditions, especially tractions free conditions at free edges, and guaranteeing the continuity of transverse stresses and electric quantities across the interfaces between different material plies, the solutions show a significant piezoelectric effect on the laminated plate near the free edges and interlaminar stresses increase magnificently in coupled circumstance compared with those of uncoupled. References [1] P. Heyliger, Exact solution for simply supported laminated piezoelectric plates. J. Appl. Mech. Trans. ASME. 64 (1997) 299-306. [2] J.S. Lee, L.Z. Jiang, Exact electroelastic analysis of piezoelectric laminae via state space approach. Int J. Solids Struct. 33 (1996) 977-990. [3] Z.Q. Cheng, C.W. Lim, S. Kitpornchai, Three-dimensional exact solution for inhomogeneous and laminated piezoelectric plates. Int. J. Eng. Sci. 37 (1999) 1425-1439. [4] K. Xu, A.K. Noor, Three-dimensional analytical solution for coupled thermoelecroelastic response of multilayered plates. Comput. Methods Appl. Mech. Eng. 126 (1995) 355-371 [5] H.Y. Sheng, H. Wang, J.Q. Ye, State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions. International Journal of Mechanical Sciences. 49 (2007) 806-818. [6] R.B. Pieps, N.J. Pagano, Interlaminar stresses in composite laminates under uniform axial
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