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CLC number: O343.8

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Received: 2005-03-20

Revision Accepted: 2005-04-08

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Cited: 4

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.9 P.967~973

10.1631/jzus.2005.A0967


A generalized plane strain theory for transversely isotropic piezoelectric plates


Author(s):  XU Si-peng, WANG Wei

Affiliation(s):  Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China

Corresponding email(s):   xu_pku@163.com

Key Words:  Plane strain, Piezoelectric plate, Circular hole


XU Si-peng, WANG Wei. A generalized plane strain theory for transversely isotropic piezoelectric plates[J]. Journal of Zhejiang University Science A, 2005, 6(9): 967~973.

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T1 - A generalized plane strain theory for transversely isotropic piezoelectric plates
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Abstract: 
Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that commonly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.

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Reference

[1] Deresiewicz, H., Royer, D., 1980. Elastic Waves in Solids. John Wiley, New York.

[2] Ding, H.J., Chen, W.Q., 2001. Three Dimensional Problems of Piezoelectricity. Nova Science Publishers, New York.

[3] Dunn, M.L., Taya, M., 1994. Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. Journal of Applied Mechanics, 61:474-475.

[4] Jin, Z.H., Hwang, K.C., 1989. An analysis of three-dimensional effects near the tip of a crack in an elastic plate. Acta Mechanica Solida Sinica, 2:387-401.

[5] Kane, T.R., Mindlin, R.D., 1956. High-frequency extensional vibrations of plates. Journal of Applied Mechanics, 23:277-283.

[6] Kotousov, A., Wang, C.H., 2002a. Three-dimensional stress constraint in an elastic plate with a notch. International Journal of Solids and Structures, 39:4311-4326.

[7] Kotousov, A., Wang, C.H., 2002b. Fundamental solutions for the generalized plane strain theory. International Journal of Engineering Science, 40:1775-1790.

[8] Kotousov, A., Wang, C.H., 2002c. Three-dimensional solutions for transversally isotropic composite plates. Composite Structures, 57:445-452.

[9] Kotousov, A., Wang, C.H., 2003. A generalized plane-strain theory for transversally isotropic plates. Acta Mechanica, 161:53-64. Li, Z.H., Guo, W.L., Kuang, Z.B., 2000. Three-dimensional elastic stress fields near notches in finite thickness plates International Journal of Solids and Structures, 37:7617-7631.

[10] Sosa, H., 1991. Plane problems in piezoelectric media with defects. International Journal of Solids and Structures, 28(4):491-505.

[11] Yang, W., Freund, L.B., 1985. Transverse shear effects for through-cracks in an elastic plate. International Journal of Solids and Structures, 21:977-994.

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