Anti-plane Moving Yoffe-crack In Functionally Graded Piezoelectric Materials

This thesis constitute of five parts.In the first part, the historical development and the basic equations of functionally graded piezoelectric materials are briefly introduced.The second part focus on the anti-plane moving Yoffe-crack problem in an infinite plane of functionally graded piezoelectric materials.The third part is about the anti-plane moving Yoffe-crack problem in a half plane of functionally graded piezoelectric materials.The fourth part lays emphasis upon anti-plane moving Yoffe-crack problem in a strip of functionally graded piezoelectric materials.The last part sums the thesis briefly and put forward to the furthermore research in the near future.Based on the three-dimensional theory of piezoelectric elasticity, the governing equations are deduced for the functionally graded piezoelectric materials, and the anti-plane fracture problems for piezoelectric medium are solved for three cases. We get the displacement, stress, electric potential and electric displacement around the crack in an infinite plane of functionally graded piezoelectric materials, a half plane of functionally graded piezoelectric materials and a strip of functionally graded piezoelectric materials by Fourier Transforms, respectively. Numerical results of the dynamic stress intensity factor, electric displacement intensity factor and electric field intensity factor near the crack tip are obtained by the way of MATLAB. Finally, the influences of different nonhomogene-ous material properties, geometrical size and the moving velocity of .the crack (v/c) on dynamic stress intensity factor, electric displacement intensity factor and electric field intensity factor are revealed.The results of this thesis may guide the design of functionally graded piezoelectric materials and forecast the function of piezoelectric medium.