Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack |
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| Institution: | 1. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan;2. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan;3. Department of Civil Engineering, National Cheng-Kung University, Tainan 70101, Taiwan;4. Bachelor Degree Program in Ocean Engineering and Technology, National Taiwan Ocean University, Keelung 20224, Taiwan;5. Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan;1. University of Glasgow, School of Engineering, Oakfield Avenue, Glasgow G12 8LT, U.K.;2. L-NESS, Politecnico di Milano, Via Anzani 42, 22100 Como, Italy;3. ETH, Electron Microscopy ETH Zurich, Wolgang-Pauli-Str. Ch-8093 Zurich, Switzerland;4. Johannes Kepler Universität, Institute of Semiconductor and Solid State Physics, A-4040 Linz, Austria;1. Department of Aviation Mechanical Engineering, China University of Science and Technology, Hsinchu 31241, Taiwan;2. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan |
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| Abstract: | Based on the complex potential approach, the two-dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied. The explicit, closed-form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole. When the elliptic hole degenerates into a crack, the field intensity factors are obtained. It is shown that the stress intensity factors are the same as that of isotropic material, while the electric displacement intensity factor depends on both the material properties and the mechanical loads, but not on the electric loads. In other words, the uniform electric loads have no influence on the field singularities. It is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials. |
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