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http://dx.doi.org/10.12989/sss.2014.14.2.225

Comprehensive piezo-thermo-elastic analysis of a thick hollow spherical shell  

Arefi, M. (Department of Solid Mechanics, Faculty of Mechanical engineering, University of Kashan)
Khoshgoftar, M.J. (Mechanical Engineering, Tarbiat Modares University)
Publication Information
Smart Structures and Systems / v.14, no.2, 2014 , pp. 225-246 More about this Journal
Abstract
The present paper develops piezo-thermo-elastic analysis of a thick spherical shell for generalized functionally graded piezoelectric material. The assumed structure is loaded under thermal, electrical and mechanical loads. The mechanical, thermal and electrical properties are graded along the radial direction based on a power function with three different non homogenous indexes. Primarily, the non homogenous heat transfer equation is solved by applying the general boundary conditions, individually. Substitution of stress, strain, electrical displacement and material properties in equilibrium and Maxwell equations present two non homogenous differential equation of order two. The main objective of the present study is to improve the relations between mechanical and electrical loads in hollow spherical shells especially for functionally graded piezoelectric materials. The obtained results can evaluate the effect of every non homogenous parameter on the mechanical and electrical components.
Keywords
piezoelectric; thick hollow spherical shell; functionally graded piezoelectric material; non homogenous;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Im, S. and Atluri, S.N. (1989), "Effects of a piezo-actuator on a finitely deformed beam subjected to general loading", AIAA. J., 27(12), 1801-1807.   DOI
2 Jonnalagadda, K.D., Blandford, G.E. and Tauchert, T.R. (1994), "Piezothermoelastic composite plate analysis using first-order shear-deformation theory", Comput. Struct., 51(1), 79-89.   DOI   ScienceOn
3 Kapuria, S., Dumir, P.C. and Sengupta, S. (1996), "Exact piezothermoelastic axisymmetric solution of a finite transversely isotropic cylindrical shell", Comput. Struct., 61(6), 1085-1099.   DOI   ScienceOn
4 Kapuria S., Dube, G.P., Dumir, P.C. and Sengupta, S. (1997), "Levy-type piezothermoelastic solution for hybrid plate by using first-order shear deformation theory", Compos. Part B - Eng., 28, 535-546.   DOI   ScienceOn
5 Khoshgoftar, M.J.G., Arani, A. and Arefi, M. (2009), "Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material", Smart. Mater. Struct., 18(11), 115007 (8pp).   DOI   ScienceOn
6 Koizumi, M. (1993), "The concept of FGM", Ceramic Transactions. Functionally. Gradient. Materials, 34, 3-10.
7 Lai, M., Rubin, D. and Krempl, E. (1999), Introduction to continuum mechanics, 3rd Ed., Buttenvorth-Heinemann press, Oxford, UK.
8 Lee, C.K. (1990), "Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part 1: governing equations and reciprocal relationships", J. Acoust. Soc. Am., 87(3), 1144-1158.   DOI
9 Lienhard IV, J.H. and Lienhard, V.J.H. (2008), A heat transfer textbook, 3rd Ed., phlogiston press, 15 Woodland Road. Lexington MA.
10 Liew, K.M., Zhang, J.Z. Li, C. and Meguid, S.A. (2005), "Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behavior of multilayered plates using the differential quadrature technique", Int. J. Solids Struct., 42, 4239-4257.   DOI   ScienceOn
11 Crawley, E.F. and De Luis, J. (1987), "Use of piezoelectric actuators as elements of intelligent structures", AIAA. J., 25(10), 1373-1385.   DOI   ScienceOn
12 Crawley, E.F. and Anderson, E.H. (1990), "Detailed models of piezoceramic actuation of beams", J. Intel. Mat. Syst. Str., 1(1), 4-25.   DOI
13 Ding, H.J. Wang, H.M. and Chen, W.Q. (2003), "Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems", Int. J. Mech. Sci., 45(6-7), 1029-1051.   DOI   ScienceOn
14 Ding, H.J. Wang, H.M. and Chen, W.Q. (2003), "Analytical solution for the electroelastic dynamics of a nonhomogeneous spherically isotropic piezoelectric hollow sphere", Arch. Appl. Mech., 73(1-2), 49 -62.   DOI   ScienceOn
15 Dai, H.L. and Wang, X. (2005), "Thermo-electro-elastic transient responses in piezoelectric hollow structures", Int. J. Solids. Struct., 42, 1151-1171.   DOI   ScienceOn
16 Dai, H.L. and Fu, Y.M. (2007), "Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads", Int. J. Pres. Ves. Pip., 84, 132-138.   DOI   ScienceOn
17 Dube, G.P., Kapuria, S. and Dumir, P.C. (1996), "Exact piezothermoelastic solution of simply-supported orthotropic flat panel in cylindrical bending", Int. J. Mech. Sci., 38(11), 1161-1177.   DOI   ScienceOn
18 Frank P, I. (1996), Introduction to heat transfer, John- Wiley Press, USA.
19 Huang, J.H. and Wu, T.L. (1996), "Analysis of hybrid multilayered piezoelectric plates", Int. J. Eng. Sci., 34(2), 171-181.   DOI   ScienceOn
20 Arefi, M. Rahimi, G.H. (2010), "Thermo elastic analy-sis of a functionally graded cylinder under internal pressure using first order shear deformation theory", Sci. Res. Essays, 5(12), 1442-1454.
21 Arefi, M. and Rahimi, G.H. (2011), "Three dimensional multi field equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity", Acta. Mech., 223(1), 63-79.
22 Arefi, M. Rahimi, G.H. and Khoshgoftar, M.J. (2011), "Optimized design of a cylinder under mechanical, magnetic and thermal loads as a sensor or actuator using a functionally graded piezomagnetic material", Int. J. Phy. Sci., 6(27), 6315-6322.
23 Arefi, M. and Rahimi, G.H. (2011), "General formulation for the thermoelastic analysis of an arbitrary structure made of functionally graded piezoelectric materials, based on the energy method", J. Mech. Eng., 62(4), 221-236.
24 Arefi, M. and Rahimi, G.H. (2012), "Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure", Smart. Struct. Syst., 9(2), 127-143.   DOI
25 Arefi, M. and Rahimi, G.H. (2012), "The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clampedeclamped FG cylinder under mechanical and thermal loads", Int. J. Pres. Ves. Pip., 96-97, 30-37.   DOI
26 Benjeddou, A. Deu, J.F. and Letombe, S. (2002), "Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation", Thin. Wall. Struct., 40(7-8), 573-593.   DOI   ScienceOn
27 Boresi, A. (1993), Advanced mechanics of materials, 5th Ed., John Wiley and Sons Press, New York, USA.
28 Wu, C.P. and Huang, S.E. (2009), "Three-dimensional solutions of functionally graded piezo-thermo-elastic shells and plates using a modified Pagano method", CMC-Comput. Mater. Continua, 12(3), 251-281.
29 Wu, C.P. and Syu, Y.S. (2007), "Exact solution of functionally graded piezoelectric shells under cylindrical bending", Int. J. Solids. Struct., 44, 6450-6472.   DOI   ScienceOn
30 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(2), 93-132.
31 Wu, C.P. and Jiang, R.Y. (2011), "The 3D coupled analysis of FGPM circular hollow sandwich cylinders under thermal loads", J. Intel. Mater. Syst. Str., 22, 691-712.   DOI
32 Wu, C.P., Chiu, K.H. and Jiang, R.Y. (2012), "A meshless collocation method for the coupled analysis of functionally graded piezo-thermo-elastic shells and plates under thermal loads", Int. J. Eng. Sci., 56, 29-48.   DOI   ScienceOn
33 Yamanouchi, M., Koizumi, M. and Shiota, I. (1990), Proceedings of the 1st international symposium on functionally gradient materials, Sendai, Japan.
34 Xu, K., Noor, A.K. and Tang, Y.Y. (1995), "Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates", Comput. Method. Appl. M., 126(3-4), 355-371.   DOI   ScienceOn
35 Ying, C. and Zhi-fei, S. (2005), "Analysis of a functionally graded piezothermoelastic hollow cylinder", J. Zhejiang. Univ-Sci. A. (Appl. Phys. & Eng.), 6(9), 956-961.   DOI
36 Mindlin, R.D. (1952), "Forced thickness-shear and flexural vibrations of piezoelectric crystal plates", J. Appl. Phys., 23(1), 83-88.   DOI
37 Ootao, Y. and Tanigawa, Y. (2007), "Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere", Compos.Struct., 81(4), 540-554.   DOI   ScienceOn
38 Mindlin, R.D. (1972), "High frequency vibrations of piezoelectric crystal plates", Int. J. Solids. Struct., 8(7), 895-906.   DOI   ScienceOn
39 Mindlin, R.D. (1984), "Frequencies of piezoelectrically forced vibrations of electroded doubly rotated quartz", Int. J. Solids. Struct., 20(2), 141-157.   DOI   ScienceOn
40 Mitchell, J.A. and Reddy, J.N. (1995), "A refined hybrid plate theory for composite laminates with piezoelectric laminate", Int. J. Solids. Struct., 32(16), 2345-2367.   DOI   ScienceOn
41 Rahimi, G.H. Arefi, M. and Khoshgoftar, M.J. (2011), "Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads", Appl. Math. Mech. (Engl. Ed), 32(8), 997-1008.   DOI   ScienceOn
42 Rahimi, G.H. Arefi, M. and Khoshgoftar, M.J. (2012), "Electro elastic analysis of a pressurized thick-walled functionally graded piezoelectric cylinder using the first order shear deformation theory and energy method", Mechanika, 18(3), 292-300.
43 Senthil, S.V. and Batra R.C. (2001), "Analysis of piezoelectric bimorphs and plates with segmented actuators", Thin. Wall. Struct., 39(1), 23-44 (doi:10.1016/S0263-8231(00)00052-5).   DOI   ScienceOn
44 Tang, Y.Y., Noor, A.K. and Xu, K. (1996), "Assessment of computational models for thermoelectroelastic multilayered plates", Comput. Struct., 61, 915-933.   DOI   ScienceOn
45 Wang, B.T. and Rogers, C.A. (1991), "Laminate plate theory for spatially distributed induced strain actuators", J. Compos. Mater., 25(4), 433-452.   DOI
46 Chen, W.Q., Lu, Y., Ye, J.R. and Cai, J.B. (2002), "3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading", Arch. Appl. Mech., 72(1), 39-51.   DOI   ScienceOn
47 Arefi, M. and Rahimi, G.H. (2011), "Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart. Struct. Syst., 8(5), 433-448.   DOI