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The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply. (English) Zbl 1119.74365
Summary: This paper is concerned with the theoretical treatment of the transient piezothermoelastic problem involving a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply in the width direction. The thermal, thermoelastic and piezoelectric constants of the strip are assumed to vary exponentially in the thickness direction. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the exact solution for a simply supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are presented in figures and table. Furthermore, the influence of the nonhomogeneity of the material and that of the electric boundary conditions are investigated.

MSC:
74F05 Thermal effects in solid mechanics
74F15 Electromagnetic effects in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Qin, Q.-H.: Fracture mechanics of piezoelectric materials. WIT, Southampton (2001)
[2] Miyamoto, Y.; Kaysser, W.A.; Rabin, B.H.; Kawasaki, A.; Ford, R.G.: Functionally graded materials: design, processing and application. Kluwer, Dordrecht (1999) pp. 247-313
[3] Wu, C.C.M.; Kahn, M.; Moy, W.: Piezoelectric ceramics with functionally gradients: a new application in material design. J Am Ceram Soc 79 (1996) 809-812
[4] Shelley, W.F.; Wan, S.; Bowman, K.J.: Functionally graded piezoelectric ceramics. Mater Sci Forum 308-311 (1999) 515-520
[5] Liu, G.R.; Tani, J.: Surface waves in functionally gradient piezoelectric plates. Trans ASME J Vib Acoust 116 (1994) 440-448
[6] Li, C.; Weng, G.J.: Yoffe-type moving crack in a functionally graded piezoelectric material. Proc R Soc Lond A 458 (2002) 381-399 · Zbl 1051.74037
[7] Li, C.; Weng, G.J.: Antiplane crack problem in functionally graded piezoelectric materials. ASME J Appl Mech 69 (2002) 481-488 · Zbl 1110.74553
[8] Jin, B.; Zhong, Z.: A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mech Res Commun 29 (2002) 217-224 · Zbl 1012.74542
[9] Wang, B.L.: A mode III crack in functionally graded piezoelectric materials. Mech Res Commun 30 (2003) 151-159 · Zbl 1026.74060
[10] Chen, J.; Liu, Z.X.; Zou, Z.Z.: Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theor Appl Fract Mech 39 (2003) 47-60
[11] Jin, B.; Soh, A.K.; Zhong, Z.: Propagation of an anti-plane moving crack in a functionally graded piezoelectric strip. Arch Appl Mech 73 (2003) 252-260 · Zbl 1068.74598
[12] Lim, C.W.; He, L.H.: Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting. Int J Mech Sci 43 (2001) 2479-2492 · Zbl 1035.74025
[13] Almajid, A.; Taya, M.: 2D-elastic Analysis of FGM Piezo-laminates under cylindrical bending. J Intell Mater Syst Struct 12 (2001) 341-351
[14] Almajid, A.; Taya, M.; Hudnut, S.: Analysis of out-of-plane displacement and stress field in a piezocomposite plate with functionally graded microstructure. Int J Solids Struct 38 (2001) 3377-3391 · Zbl 1090.74549
[15] Wu, X.H.; Chen, C.; Shen, Y.P.; Tian, X.G.: A high order theory for functionally graded piezoelectric shells. Int J Solids Struct 39 (2002) 5325-5344 · Zbl 1008.74518
[16] Chen, W.Q.; Ding, H.J.: On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech 153 (2002) 207-216 · Zbl 1008.74038
[17] Chen, W.Q.; Ding, H.J.; Liang, J.: The exact elasto-electric field of a rotating piezoceramic spherical shell with a functionally gradient property. Int J Solids Struct 38 (2001) 7015-7027 · Zbl 1013.74024
[18] Chen, W.Q.; Lu, Y.; Ye, G.R.; Cai, J.B.: 3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading. Arch Appl Mech 72 (2002) 39-51 · Zbl 1017.74019
[19] Zhong, Z.; Shang, E.T.: Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate. Int J Solids Struct 40 (2003) 5335-5352 · Zbl 1060.74568
[20] Wang, B.L.; Noda, N.: Design of a smart functionally graded thermopiezoelectric composite structure. Smart Mater Struct 10 (2001) 189-193
[21] Wu, X.H.; Shen, Y.P.; Chen, C.: An exact solution for functionally graded piezothermoelastic cylindrical shell as sensors or actuators. Mater Lett 57 (2003) 3532-3542
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