State-space approach for bending analysis of functionally graded piezoelectric plate using five-variable refined plate theory

Document Type : Research Article

Authors

Department of Mechanical Engineering, Shiraz University of Technology, Shiraz, Iran

Abstract

In this paper, an analytical solution for bending analysis of functionally-graded piezoelectric plate with two simply-supported parallel edges and two other arbitrary boundary conditions under uniformly-distributed transverse loading is presented. The five-variable refined plate theory is employed for describing the displacement field. This theory, despite the few numbers of unknown variables, predicts a parabolic distribution for transverse shear stresses across the thickness and also considers the thickness-stretching effect. The governing equations are obtained using Hamilton’s principle and Maxwell's equation. The Levy-type solution in conjunction with the state-space approach is used to solve them. Comparing the results with those obtained by the higher-order shear theories and Abaqus finite element simulation confirms the accuracy and efficiency of the proposed method. It can be seen that for the length-to-thickness ratio of 10 and the power-law index of 0.5, the value of non-dimensional deflection of the plate with the clamped boundary condition is 0.3327, which has the largest amount of stiffness, while the value of the non-dimensional deflection of the plate with two parallel free boundary condition edges having the lowest amount of stiffness is 2.2036. In addition, for the plate with a clamped boundary condition and length-to-thickness ratio of 10, with the increase of the power index from 0.5 to 10, the value of displacement changes from 0.3327 to 0.3545, which means an increase of about 6%.

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References

[1] M. Benchohra, H. Driz, A. Bakora, A. Tounsi, E. Adda Bedia, S.R. Mahmoud, A new quasi-3D sinusoidal shear deformation theory for functionally graded plates, Structural engineering and mechanics: An international journal, 65(1) (2018) 19-31.
[2] S.-H. Chi, Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis, International Journal of Solids and Structures, 43(13) (2006) 3657-3674.
[3] M. Shariati, M. Shishehsaz, R. Mosalmani, Stress-driven Approach to Vibrational Analysis of FGM Annular‎ Nano-plate based on First-order Shear Deformation Plate Theory, Journal of Applied and Computational Mechanics,  in-press (2023) 1-23.
[4] J. Reddy, Analysis of functionally graded plates, International Journal for numerical methods in engineering, 47(1‐3) (2000) 663-684.
[5] P.V. Vinh, Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method, Journal of Sandwich Structures & Materials, 24(2) (2022) 860-899.
[6] M. Li, C.G. Soares, R. Yan, A novel shear deformation theory for static analysis of functionally graded plates, Composite Structures, 250 (2020) 112559.
[7] R.P. Shimpi, Refined plate theory and its variants, AIAA journal, 40(1) (2002) 137-146.
[8] R. Shimpi, H. Patel, A two variable refined plate theory for orthotropic plate analysis, International Journal of Solids and Structures, 43(22-23) (2006) 6783-6799.
[9] S.-E. Kim, H.-T. Thai, J. Lee, A two variable refined plate theory for laminated composite plates, Composite Structures, 89(2) (2009) 197-205.
[10] H.-T. Thai, D.-H. Choi, Improved refined plate theory accounting for effect of thickness stretching in functionally graded plates, Composites Part B: Engineering, 56 (2014) 705-716.
[11] M. Bennoun, M.S.A. Houari, A. Tounsi, A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates, Mechanics of Advanced Materials and Structures, 23(4) (2016) 423-431.
[12] Y. Li, J. Ren, W. Feng, Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field, Applied Mathematical Modelling, 47 (2017) 63-75.
[13] M. Arefi, E.M.-R. Bidgoli, R. Dimitri, M. Bacciocchi, F. Tornabene, Application of sinusoidal shear deformation theory and physical neutral surface to analysis of functionally graded piezoelectric plate, Composites Part B: Engineering, 151 (2018) 35-50.
[14] A.M. Zenkour, Z.S. Hafed, Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory, Mechanics of Advanced Materials and Structures, 27(18) (2020) 1551-1562.
[15] Y. Xue, J. Li, F. Li, Z. Song, Active control of plates made of functionally graded piezoelectric material subjected to thermo-electro-mechanical loads, International Journal of Structural Stability and Dynamics, 19(09) (2019) 1950107.
[16] N.T. Dung, P.V. Minh, H.M. Hung, D.M. Tien, The third-order shear deformation theory for modeling the static bending and dynamic responses of piezoelectric bidirectional functionally graded plates, Advances in Materials Science and Engineering, 2021 (2021) 1-15.
[17] P. Kumar, S.P. Harsha, Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment, Journal of Composite Materials, 56(24) (2022) 3749-3767.
[18] J.S. Lee, L.Z. Jiang, Exact electroelastic analysis of piezoelectric laminae via state space approach, International Journal of Solids and Structures, 33(7) (1996) 977-990.
[19] H. Sheng, H. Wang, J. Ye, State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions, International Journal of Mechanical Sciences, 49(7) (2007) 806-818.
[20] A. Alibeigloo, R. Madoliat, Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature, Composite Structures, 88(3) (2009) 342-353.
[21] A. Alibeigloo, Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock, Journal of Thermal Stresses, 42(11) (2019) 1357-1375.
[22] M. Feri, M. Krommer, A. Alibeigloo, Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers, Mechanics Based Design of Structures and Machines,  (2021) 1-25.
[23] J.-m. ZHANG, Z.-h. MAO, F. Xin, L.-l. ZHANG, G. Yang, Free Vibration of Three-Dimensional Piezoelectric Cubic Quasicrystal Plates, in:  2020 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA), IEEE, 2021, pp. 253-257.
[24] A. Alibeigloo, M. Talebitooti, Three dimensional transient coupled thermoelasticity analysis of FGM cylindrical panel embedded in piezoelectric layers, Mechanics of Smart Structures,  in-press (2021) 1-20.
[25] J. Rouzegar, N. Salmanpour, F. Abad, L. Li, An analytical state-space solution for free vibration of sandwich piezoelectric plate with functionally graded core, Scientia Iranica, 29(2) (2022) 502-533.
[26] M.H. Sadd, Elasticity: theory, applications, and numerics, 2nd Edition, Academic Press, 2009.
[27] S. Shiyekar, T. Kant, Higher order shear deformation effects on analysis of laminates with piezoelectric fibre reinforced composite actuators, Composite structures, 93(12) (2011) 3252-3261.
[28] M.A. Farsangi, A. Saidi, R. Batra, Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates, Journal of Sound and Vibration, 332(22) (2013) 5981-5998.
[29] M.A. Farsangi, A. Saidi, Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers, Smart materials and structures, 21(9) (2012) 094017.
[30] J. Rouzegar, R. Koohpeima, F. Abad, Dynamic analysis of laminated composite plate integrated with a piezoelectric actuator using four-variable refined plate theory, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 44 (2020) 557-570.
[31] J. Rouzegar, F. Abad, Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory, Thin-Walled Structures, 89 (2015) 76-83.
[32] P.A. Demirhan, V. Taskin, Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach, Composites Part B: Engineering, 160 (2019) 661-676.
[33] J.N. Franklin, Matrix theory, 1st   Edition, Courier Corporation, 2012.
[34] A.M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, 30(1) (2006) 67-84.
[35] H.-T. Thai, D.-H. Choi, Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates, Archive of Applied Mechanics, 83 (2013) 1755-1771.
[36] P.A. Demirhan, V. Taskin, Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory, Composite Structures, 177 (2017) 80-95.
[37] M. Bodaghi, M. Shakeri, An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads, Composite Structures, 94(5) (2012) 1721-1735.
Amirkabir Journal of Mechanical Engineering
Volume 55, Issue 2
May 2023
Pages 213-234

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