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Research Papers

Three-Dimensional Piezoelectricity Solutions for Uniformly Loaded Circular Plates of Functionally Graded Piezoelectric Materials With Transverse Isotropy

[+] Author and Article Information
X.-Y. Li

School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: zjuparis6@hotmail.com

H.-J. Ding

Department of Civil Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: dinghj@zju.edu.cn

W.-Q. Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China
e-mail: chenwq@zju.edu.cn

P.-D. Li

School of Mechanics and Engineering,
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 80(4), 041007 (May 16, 2013) (12 pages) Paper No: JAM-12-1027; doi: 10.1115/1.4007968 History: Received January 23, 2012; Revised June 29, 2012; Accepted October 30, 2012

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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Figures

Grahic Jump Location
Fig. 1

A circular plate subject to a uniform load

Grahic Jump Location
Fig. 2

Variations of dimensionless physical quantities along the axisymmetric axis (ξ = 0) of the FGM plate with material coefficients varying according to Eq. (78). Data are for: radial displacement U (a), normal displacement W¯ (b), normal stress Σζζ (c), shear stress Σξζ (d), radial stress Σξξ (e). Data are for: present solutions (solid line), FEM results (▪) and those given by Li et al. [31] (•).

Grahic Jump Location
Fig. 3

Distributions of the electro-elastic field in the FGPM with material properties varying according to Eq. (80)

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