Browse > Article
http://dx.doi.org/10.12989/sss.2015.16.5.781

Coupled electro-elastic analysis of functionally graded piezoelectric material plates  

Wu, Chih-Ping (Department of Civil Engineering, National Cheng Kung University)
Ding, Shuang (Department of Civil Engineering, National Cheng Kung University)
Publication Information
Smart Structures and Systems / v.16, no.5, 2015 , pp. 781-806 More about this Journal
Abstract
A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.
Keywords
three-dimensional analysis; coupled electro-elastic analysis; static; finite layer methods; functionally graded materials; piezoelectric plates;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Arefi, M. (2014), "Generalized shear deformation theory for the thermo elastic analyses of the functionally graded cylindrical shells", Struct. Eng. Mech., 50(3), 403-417.   DOI
2 Arefi, M., Rahimi, G.H. (2014), "Application of shear deformation theory for two dimensional electro-elastic analysis of a FGP cylinder", Smart Struct. Syst., 13(1), 1-24.   DOI
3 Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2012), "Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electric loads in the magnetic field", Smart Struct. Syst., 9(5), 427-439.   DOI   ScienceOn
4 Ballhause, D., D'Ottavio, M., Kroplin, B. and Carrera, E. (2005), "A unified formulation to assess multilayered theories for piezoelectric plates", Comput. Struct., 83(15-16), 1217-1235.   DOI   ScienceOn
5 Brischetto, S. and Carrera, E. (2010), "Advanced mixed theories for bending analysis of functionally graded plates", Comput. Struct. 88(23-24), 1474-1483.   DOI   ScienceOn
6 Brischetto, S. and Carrera, E. (2009), "Refined 2D models for the analysis of functionally graded piezoelectric plates", J. Intell. Mat. Syst. Str., 20, 1783-1797.   DOI
7 Brischetto, S. and Carrera, E. (2012), "Coupled thermo-electro-mechanical analysis of smart plates embedding composite and piezoelectric layers", J. Therm. Stresses, 35(9), 766-804.   DOI
8 Carrera, E. (2003), "Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Method. E., 10(3), 215-296.   DOI
9 Carrera, E. and Boscolo, M. (2007), "Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates", Int. J. Numer. Meth. Eng., 70(10), 1135-1181.   DOI
10 Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46(1), 194-203.   DOI
11 Carrera, E., Buttner, A. and Nali, P. (2010), "Mixed elements for the analysis of anisotropic multilayered piezoelectric plates", J. Intell. Mat. Syst. Str., 21(7), 701-717.   DOI
12 Kashtalyan, M. and Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos. Struct., 87(1), 36-43.   DOI
13 Lu, P., Lee, H.P. and Lu, C. (2005), "An exact solution for functionally graded piezoelectric laminates in cylindrical bending", Int. J. Mech. Sci., 47(3), 437-438.   DOI
14 Liew, K.M., He, X.Q., Ng, T.Y. and Kitipornchai, S. (2003a), "Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators", Comput. Mech., 31(3), 350-358.   DOI
15 Liew, K.M., Sivashanker, S., He, X.Q. and Ng, T.Y. (2003b), "The modelling and design of smart structures using functionally graded materials and piezoelectric sensor/actuator patches", Smart Mater. Struct., 12(4), 647-655.   DOI
16 Loja, M.A.R., Mota Soares, C.M. and Barbosa, J.I. (2013), "Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip method", Compos. Struct., 96, 606-615.   DOI
17 Lu, P., Lee, H.P. and Lu, C. (2006), "Exact solutions for simply supported functionally graded piezoelectric laminates by Stroh-like formalism", Compos. Struct., 72(3), 352-363.   DOI
18 Ootao, Y. and Ishihara, M. (2013), "Asymmetric transient thermal stress of a functionally graded hollow cylinder with piecewise power law", Struct. Eng. Mech., 47(3), 421-442.   DOI
19 Pan, E. (2003), "Exact solution for functionally graded anisotropic elastic composite laminates", J. Compos. Mater., 37(21), 1903-1920.   DOI
20 Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339.   DOI   ScienceOn
21 Reissner, E. (1984), "On a certain mixed variational theorem and a proposed application", Int. J. Numer. Meth. Eng., 20(7), 1366-1368.   DOI   ScienceOn
22 Sladek, J., Sladek, V., Stanak, P., Wen, P.H. and Atluri, S.N. (2012), "Laminated elastic plates with piezoelectric sensors and actuators", CMES-Comput. Model. Eng. Sci., 85, 543-572.
23 Reissner, E. (1986), "On a mixed variational theorem and on a shear deformable plate theory", Int. J. Numer. Meth. Eng., 23(2), 193-198.   DOI   ScienceOn
24 Saravanos, D.A. and Heyliger, P.R. (1999), "Mechanics and computational models for laminated piezoelectric beams, plates, and shells", Appl. Mech. Rev., 52(10), 305-320.   DOI
25 Sladek, J. Sladek, V., Stanak, P. and Pan, E. (2010), "The MLPG for bending of electroelastic plates", CMES-Comput. Model. Eng. Sci., 64, 267-297.
26 Sladek, J., Sladek, V., Stanak, P., Zhang, C. and Wunshe, M. (2013), "Analysis of bending of circular piezoelectric plates with functionally graded material properties by a MLPG method", Eng. Struct., 47, 81-89.   DOI
27 Tang, Y.Y., Noor, A.K. and Xu, K. (1996), "Assessment of computational models for thermoelectroelastic multilayered plates", Comput. Struct., 61(5), 915-933.   DOI
28 Tsai, Y.H. and Wu, C.P. (2008), "Dynamic responses of functionally graded magneto-electro-elastic shells with open-circuit surface conditions", Int. J. Eng. Sci., 46(9), 843-857.   DOI
29 Woodward, B. and Kashtalyan, M. (2010), "Bending response of sandwich panels with graded core: 3D elasticity analysis", Mech. Adv. Mater. Struct., 17(8), 586-594.   DOI
30 Wu, C.P. and Chang, Y.T. (2012), "A unified formulation of RMVT-based finite cylindrical layer methods for sandwich circular hollow cylinders with an embedded FGM layer", Compos. Part B: Eng., 43(8), 3318-3333.   DOI
31 Wu, C.P. and Li, H.Y. (2013b), "An RMVT-based finite rectangular prism method for the 3D analysis of sandwich FGM plates with various boundary conditions", CMC-Comput. Mater. Continua, 34, 27-62.
32 Wu, C.P. and Li, H.Y. (2010a), "The RMVT-and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates", Compos. Struct., 92(10), 2476-2496.   DOI   ScienceOn
33 Wu, C.P. and Li, H.Y. (2010b), "RMVT-and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates", CMC-Comput. Mater. Continua, 19, 155-198.
34 Wu, C.P. and Li, H.Y. (2013a), "RMVT-based finite cylindrical prism methods for multilayered functionally graded circular hollow cylinders with various boundary conditions", Compos. Struct., 100, 592-608.   DOI
35 Wu, C.P. and Syu, Y.S. (2007), "Exact solutions of functionally graded piezoelectric shells under cylindrical bending", Int. J. Solids Struct., 44(20), 6450-6472.   DOI
36 Wu, C.P. and Tsai, Y.H. (2007), "Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux", Int. J. Eng. Sci., 45(9), 744-769.   DOI
37 Wu, C.P. and Tsai, Y.H. (2009), "Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation", J. Eng. Math., 63(1), 95-119.   DOI
38 Wu, C.P., Chiu, K.H. and Wang, Y.M. (2008), "A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells", CMC-Comput. Mater. Continua, 8, 93-132.
39 Wu, X.H., Chen, C. and Shen, Y.P. (2002), "A high order theory for functionally graded piezoelectric shells", Int. J. Solids Struct., 39(20), 5325-5344.   DOI
40 Wu, C.P., Fan, T.Y. and Li, H.Y. (2014), "Reissner mixed variational theorem-based finite cylindrical layer methods for the 3D free vibration analysis of sandwich circular hollow cylinders with an embedded FGM layer", J. Vib. Control, 20(8), 1199-1223.   DOI
41 Zhang, T., Shi, Z. (2010), "Exact analyses for two kinds of piezoelectric hollow cylinders with graded properties", Smart Struct. Syst., 6(8), 975-989.   DOI
42 Zhong, Z. and Shang, E.T. (2003), "Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate", Int. J. Solids Struct., 40(20), 5335-5352.   DOI
43 Zhong, Z. and Yu, T. (2006), "Vibration of a simply supported functionally graded piezoelectric rectangular plate", Smart Mater. Struct., 15(5), 1404-1412.   DOI