Abstract
First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three “harmonic functions”. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.
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References
Y. Shindo, E. Ozava and J. P. Nowacki, Singular stress and electric fields of a cracked piezoelectric strip,International Journal of Applied Electronic Materials.1 (1990), 77–87.
Z. Suo, C. M. Kuo, D. M. Barnett and J. R. Willis, Fracture mechanics for piezoelectric ceramics,Journal of the Mechanics and Physics of Solids,40 (1992), 739–765.
M. L. Dunn and M. Taya, An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities.Proceedings of the Royal Society of London, Series A,443 (1993), 245–287.
T. Y. Chen, Exact relations of inclusions in piezoelectric media,International Journal of Engineering Science,32 (1994). 265–287.
K. H. Sung, C. Keilers and F. K. Chang, Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators,AIAA Journal,30, (1993), 772–780.
Z. Wang and B. Zheng, The general solution of three-dimensional problem in piezoelectric media,International Journal of Solids and Structures,32 (1995), 105–115.
H. J. Ding, B. Chen and J. Liang, General solutions for coupled equations for piezoelectric media,International Journal of Solids and Structures,33 (1996), 2283–2298.
S. P. Timoshenko and J. N. Goodier,Theory of Elasticity, McGraw-Hill (1970).
S. G. Lekhniskii,Theory of Anisotropic Plate (Hu Haichang transl.), Science Press (1955), (Chinese version)
H. J. Ding and Y. Li, Plane problems of cylindrically anisotropic elasticity,Chinese Journal of Applied Mechanics,11 (1994), 11–18. (in Chinese)
H. A. Sosa and M. A. Castro, On concentrated loads at the boundary of a piezoelectric half-plane,Journal of the Mechanics and Physics of Solids,42 (1994), 1105–1122.
H. A. Sosa and M. A. Castro, Electroelastic analysis of piezoelectric laminated structures,Applied Mechanics Review,46 (1993), 21–28.
R. A. Eubanks and E. Sternberg, On the axisymmetric problem of elastic theory for a medium with transverse isotropy,Journal of Rational Mechanics Analysis,3 (1954), 89–101.
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Project supported by the National Natural Science Foundation of China
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Haojiang, D., Guoqing, W. & Weiqiu, C. General solution of plane problem of piezoelectric media expressed by “harmonic functions”. Appl Math Mech 18, 757–764 (1997). https://doi.org/10.1007/BF00763127
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DOI: https://doi.org/10.1007/BF00763127