This paper considers the bending of a uniformly loaded transversely isotropic piezoelectric circular plate with material properties being arbitrary functions of the thickness coordinate. The displacements and electric potential are expressed in terms of appropriate polynomials of r, the radial coordinate, with coefficients being undetermined functions of z, the axial coordinate. The differential equations satisfied by eight z-dependent functions are derived for the general case. For the uniform load, the eight functions can be obtained through a step-by-step integration with properly incorporating the boundary conditions at the upper and lower surfaces of the plate. The three-dimensional solutions for functionally graded piezoelectric circular plates with simply-supported or clamped boundary are presented. These solutions can be readily degenerated into those for a homogenous circular plate. Three numerical examples are finally given to show the validity of the analysis, the effect of material heterogeneity and the merits of the present analyses. Since no ad hoc hypotheses on the distribution of the elastic and electric fields are introduced, the present three-dimensional solutions could provide a useful way for checking the validity of various approximate theories and numerical methods.
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July 2013
Research-Article
Three-Dimensional Piezoelectricity Solutions for Uniformly Loaded Circular Plates of Functionally Graded Piezoelectric Materials With Transverse Isotropy
X.-Y. Li,
X.-Y. Li
1
School of Mechanics and Engineering,
e-mail: zjuparis6@hotmail.com
Southwest Jiaotong University
,Chengdu 610031
, China
e-mail: zjuparis6@hotmail.com
1Corresponding author.
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W.-Q. Chen,
W.-Q. Chen
Department of Engineering Mechanics,
e-mail: chenwq@zju.edu.cn
Zhejiang University
,Hangzhou 310027
, China
e-mail: chenwq@zju.edu.cn
Search for other works by this author on:
P.-D. Li
P.-D. Li
School of Mechanics and Engineering,
e-mail: lipeidongde@163.com
Southwest Jiaotong University
,Chengdu 610031
, China
e-mail: lipeidongde@163.com
Search for other works by this author on:
X.-Y. Li
School of Mechanics and Engineering,
e-mail: zjuparis6@hotmail.com
Southwest Jiaotong University
,Chengdu 610031
, China
e-mail: zjuparis6@hotmail.com
H.-J. Ding
W.-Q. Chen
Department of Engineering Mechanics,
e-mail: chenwq@zju.edu.cn
Zhejiang University
,Hangzhou 310027
, China
e-mail: chenwq@zju.edu.cn
P.-D. Li
School of Mechanics and Engineering,
e-mail: lipeidongde@163.com
Southwest Jiaotong University
,Chengdu 610031
, China
e-mail: lipeidongde@163.com
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 23, 2012; final manuscript received June 29, 2012; accepted manuscript posted October 30, 2012; published online May 16, 2013. Assoc. Editor: Chad Landis.
J. Appl. Mech. Jul 2013, 80(4): 041007 (12 pages)
Published Online: May 16, 2013
Article history
Received:
January 23, 2012
Revision Received:
June 29, 2012
Accepted:
October 30, 2012
Citation
Li, X., Ding, H., Chen, W., and Li, P. (May 16, 2013). "Three-Dimensional Piezoelectricity Solutions for Uniformly Loaded Circular Plates of Functionally Graded Piezoelectric Materials With Transverse Isotropy." ASME. J. Appl. Mech. July 2013; 80(4): 041007. https://doi.org/10.1115/1.4007968
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