Static Analysis of Functionally Graded Piezoelectric Plates under Electro-thermo-mechanical Loading Using a Meshfree Method Based on RPIM

[1] J. Belinha, A.L. Araújo, A.J.M. Ferreira, L.M.J.S. Dinis, R.M. Natal Jorge, The analysis of laminated
plates using distinct advanced discretization meshless techniques, Compos. Struct., 143 (2016) 165-179.
[2] P. Zhu, K.M. Liew, Free vibration analysis of moderately thick functionally graded plates by local
Kriging meshless method, Compos. Struct., 93(11) (2011) 2925-2944.
[3] P.J.C. Branco, J.A. Dente, On the electromechanics of a piezoelectric transducer using a bimorph cantilever undergoing asymmetric sensing and actuation, Smart Mater. Struct., 13(4) (2004) 631-642.
[4] H. Gu, Y. Moslehy, D. Sanders, G. Song, Y.L. Mo, Multi-functional smart aggregate-based structural
health monitoring of circular reinforced concrete columns subjected to seismic excitations, Smart
Mater. Struct., 19(6) (2010) 065026.
[5] K.M. Liew, X.Q. He, T.Y. Ng, S. Sivashanker, Active control of FGM plates subjected to a temperature gradient: Modelling via finite element method based on FSDT, Int. J. Numer. Methods Eng., 52(11) (2001) 1253-1271.
[6] X. Guo, D. Fang, A.K. Soh, H.C. KIM, J.J. Lee, Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method, Acta Mech. Sin., 22(1) (2006) 34-39.
[7] X.H.Wu, Y.P. Shen, X.G. Tian, A high order theory for functionally graded piezoelectric shells, Int. J. Numer. Methods Eng., 39(20) (2002) 5325-5344.
[8] L. Qirong, L. Zhengxing, J. Zhanli, A close-form solution to simply supported piezoelectric beams under uniform exterior pressure, Appl. Math. Mech., 21(6) (2000) 681-690.
[9] L. Qi-rong, L. Zheng-xing, W. Zong-li, Analysis of beams with piezoelectric actuators, Appl. Math.
Mech., 22(9) (2001) 1074-1081.
[10] Z. Lin-nan, S. Zhi-fei, Analytical solution of a simply supported piezoelectric beam subjected to a
uniformly distributed loading, Appl. Math. Mech., 24(10) (2003) 1215-1223.
[11] A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, P.A.L.S. Martins, Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method, Compos. Struct., 69(4) (2005) 449-457.
[12] J. Yang, H.J. Xiang, Thermo-electro-mechanical characteristics of functionally graded piezoelectric
actuators, Smart Mater. Struct., 16(3) (2007) 784-797.
[13] X.L. Chen, Z.Y. Zhao, K.M. Liew, Stability of piezoelectric FGM rectangular plates subjected to non-uniformly distributed load, heat and voltage, Adv. Eng. Software, 39(2) (2008) 121-131.
[14] Z. Yan, M. Zaman, L. Jiang, Thermo-electromechanical analysis of a curved functionally graded
piezoelectric actuator with sandwich structure, Materials, 4(12) (2011) 2151-2170.
[15] A. Komeili, A.H. Akbarzadeh, A. Doroushi, M.R. Eslami, Static analysis of functionally graded piezoelectric beams under thermo-electro-mechanical loads, Adv. Eng. Software, 3 (2011) 153731.
[16] J. Singh, K.K. Shukla, Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method, Eng. Anal. Boundary Elem., 36(12) (2012) 1819-1827.
[17] P. Staňák, V. Sládek, J. Sládek, S. Krahuleca, L. Sátor, Application of patch test in meshless analysis of continuously non-homogeneous piezoelectric circular plate, Appl. Comput. Anal., 7(1) (2013) 65-76.
[18] J. Sládek, V. Sládek„ P. Stanak, C. Zhang, M. Wünsche, Analysis of the bending of circular piezoelectric plates with functionally graded material properties by a MLPG method, Eng. Struct., 47 (2013) 81-89.
[19] P. Zhu, L.W. Zhang, K.M. Liew, Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation, Compos. Struct., 107 (2014) 298-314.
[20] L. Sator, V. Sladek, J. Sladek, Coupling effects in elastic analysis of FGM composite plates by meshfree methods, Compos. Struct., 115 (2014) 100-110.
[21] L. Sator, J. Sládek, V. Sládek, D.L. Young, Elastodynamics of FGM plates by mesh-free method, Compos. Struct., 140 (2016) 309-322.
[22] P. Staňák, J. Sládek, V. Sládek, S. Krahulec, Numerical MLPG Analysis of Piezoelectric Sensor in
Structures, Slovak J. Civ. Eng., 22(2) (2014) 15-20.
[23] P. Stanak, J. Sládek, V. Sládek„ A. Tadeu, Three-Dimensional Meshless Modelling of Functionally Graded Piezoelectric Sensor, In: Březina T., Jabloński R. (eds) Mechatronics 2013, Cham: Springer International Publishing, (2014).
[24] S. Li, L. Yao, S. Yi, W. Wang, A meshless radial basis function based on partition of unity method
for piezoelectric structures, Math. Prob. Eng., 2016 (2016) 7632176.
[25] S. Mikaeeli, B. Behjat, Three-dimensional analysis of thick functionally graded piezoelectric plate using EFG method, Compos. Struct., 154 (2016) 591-599.
[26] M.R. Barati, A.M. Zenkour, Electro-thermoelastic vibration of plates made of porous functionally
graded piezoelectric materials under various boundary conditions, J. Vib. Control, 24(10) (2016) 1910-1926.
[27] M.R. Barati, H. Shahverdi, A.M. Zenkour, Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory, Mech. Adv. Mater. Struct., 24(12) (2017) 987-998.
[28] P. Phung Van, T. Cuong Le, H. Nguyen-Xuan, M. Abdel Wahab, Nonlinear transient isogeometric
analysis of FG-CNTRC nanoplates in thermal environments, Compos. Struct., 201 (2018) 882-892.
[29] A.M. Zenkour, M.H. Aljadani, Thermo-electrical buckling response of actuated functionally graded
piezoelectric nanoscale plates, Results Phys., 13 (2019) 102192.
[30] S.Q. Zhang, Y.S. Gao, G.Z. Zhao, Y.J. Yu, M.Chen, X.F. Wang, Geometrically nonlinear analysis of CNT-reinforced functionally graded composite plates integrated with piezoelectric layers, Compos. Struct., 234 (2020) 111694.
[31] H.H. Phan-Dao, C.H. Thai, J. Lee, H. NguyenXuan, Analysis of laminated composite and sandwich plate structures using generalized layerwise HSDT and improved meshfree radial point interpolation method, Aerosp. Sci. Technol., 58 (2016) 641-660.
[32] G.R. Liu, Mesh Free Methods: Moving Beyond The Finite Element Method, CRC Press, New York, (2009).
[33] G.R. Liu, Y.T. Gu, An Introduction to Meshfree Methods and Their Programming, Springer, (2005).
[34] M.A. Golberg, C.S. Chen, H. Bowman, Some recent results and proposals for the use of radial basis
functions in the BEM, Eng. Anal. Boundary Elem., 23(4) (1999) 285-296.
[35] B. Yildirim, S. Dag, F. Erdogan, Three dimensional fracture analysis of FGM coatings under thermomechanical loading, Int. J. Fract., 132(4) (2005) 371-397.
[36] J. Reddy, Analysis of functionally graded plates, Int. J. Numer. Methods Eng., 47(1-3) (2000) 663-684.
[37] T.Y. Ng, K.Y. Lam, K.M. Liew, J.N. Reddy, Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading, Int. J. Numer. Methods Eng., 38(8) (2001) 1295-1309.
[38] J. Yang, H.J. Xiang, Thermo-electro-mechanical characteristics of functionally graded piezoelectric
actuators, Smart Mater. Struct., 16(3) (2007) 784-797.
[39] J.N. Reddy, On laminated composite plates withintegrated sensors and actuators, Eng. Struct., 21(7) (1999) 568-593.
[40] M.H. Babaei, G. Akhras, Graded piezoelectric cylinders subjected to high electric fields and comparison of their frequency response with piezoelectric plates, Meccanica, 49(6) (2014) 1527-1538.
[41] A. Armin, I. Shafieenejad, N. Moallemi, A.B. Novinzadeh, Comparison between hpm and finite
fourier solution in static analysis of fgpm beam under thermal load, J. Theor. Appl. Mech., 48(1) (2010) 173-189.
[42] K. Takagi, J.F. Li, S. Yokoyama, R. Watanabe, A. Almajid, M.Taya, Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator, Sci. Technol. Adv. Mater., 3(2) (2002) 217-224.
[43] M. Taya, A.A. Almajid, M. Dunn, H. Takahashi, Design of bimorph piezo-composite actuators with
functionally graded microstructure, Sens. Actuators A, 107(3) (2003) 248-260.
[44] D. Varelis, D.A. Saravanos, Non-linear coupled multi-field mechanics and finite element for active
multi-stable thermal piezoelectric shells, Int. J. Numer. Methods Eng., 76(1) (2008) 84-107.
[45] S. Cen, A.K. Soh, Y.Q. Long, Z.H.Yao, A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates, Compos. Struct., 58(4) (2002) 583-599.