本文提出功能性梯度壓電材料(Functionally Graded Piezoelectric Material, FGPM)疊層簡支承中空圓柱殼受電彈外力作用下之三維耦合分析。功能性梯度壓電材料層的材料性質為非均質性，且隨厚度座標方向依照指數律進行變化。為分析功能性梯度壓電材料疊層圓柱殼，本文引入改良Pagano方法，其改良之處如下：以混合型理論推導替代以位移為基礎的推導方式；將系統方程式的虛數解轉換為相對應的實數解；應用連續近似法，將功能性梯度壓電材料疊層圓柱殼模擬為一多層均質壓電材料圓柱殼，每一層的厚度相等且較圓心至中曲面處之半徑為小，材料係數以厚度平均值的概念求取；使用傳遞矩陣法，可逐層求解系統方程式，計算效率更為省時。本文並對寬厚比、封閉與開放迴路及材料性質梯度指數等，探討其於功能性梯度壓電材料疊層圓柱殼各場變量的影響。

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transfer each FGPM layer to be a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a propagator matrix method is developed, so that the general solutions of system equations can be obtained layer-by-layer, which is significantly less time-consuming than usual. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.

Akhras G., Li W.C., Three-dimensional static, vibration and stability analysis of piezoelectric composite plates using a finite layer method, Smart Mater. Struct. 16, 561_569, (2007).
Akhras G., Li W.C., Three-dimensional thermal buckling analysis of piezoelectric composite plates using the finite layer method, Smart Mater. Struct. 17, 1_8, (2008).
Alibeigloo A., Kani A.M., 3D free vibration analysis of laminated cylindrical shell integrated piezoelectric layers using the differential quadrature method, Appl. Math. Modelling 34, 4123_4137, (2010).
Bufler H., Theory of elasticity of a multilayered medium, J. Elasticity 1, 125_143, (1971).
Cheung Y.K., Jiang C.P., Finite layer method in analyses of piezoelectric composite laminates, Comput. Methods Appl. Mech. Eng. 191, 879_901, (2001).
Dai H.L., Hong L., Fu Y.M., Xiao X., Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder, Appl. Math. Modelling 34, 343_357, (2010).
Fan J.R., Zhang J., Analytical solutions for thick doubly curved laminated shells, J. Eng. Mech. 118, 1338_1356, (1992).
Heyliger P., Static behavior of laminated elastic/piezoelectric plates, AIAA J. 32, 2481_2484, (1994).
Heyliger P., Saravanos D.A., Exact free-vibration analysis of laminated plates witembedded piezoelectric layers, J. Acoust. Soc. Am. 98, 1547_1557, (1995).
Heyliger P., Brooks S., Free vibration of piezoelectric laminates in cylindrical bending, Int. J. Solids Struct. 32, 2945_2960, (1995).
Heyliger P., Brooks S., Exact solutions for laminated piezoelectric plates in cylindrical bending, J. Appl. Mech. 63, 903_910, (1996).
Heyliger P., A note on the static behavior of simply-supported laminated piezoelectric cylinders, Int. J. Solids Struct. 34, 3781_3794, (1997).
Heyliger P., Exact solutions for simply supported piezoelectric plates, J. Appl. Mech. 64, 299_306, (1997).
Kapuria S., Sengupta S., Dumir P.C., Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load. Arch. Appl. Mech. 67, 320_330, (1997).
Kapuria S., Dumir P.C., Sengupta S., Nonaxisymmetric exact piezothermoelastic solution for laminated cylindrical shell, AIAA J. 35, 1792_1795, (1997).
Pagano N.J., Exact solutions for composite laminates in cylindrical bending, J. Compos. Mater. 3, 398_411, (1969).
Pagano N.J., Exact solutions for rectangular bidirectional composites and sandwich plates, J. Compos. Mater. 4, 20_34, (1970).
Ramirez F., Heyliger P.R., Pan E., Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach, Compos Part B: Eng. 37, 10_20, (2006).
Ramirez F., Heyliger P.R., Pan E., Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates, Mech. Adv. Mater. Struct. 13, 249_266, (2006).
Ren J.G., Exact solutions for laminated cylindrical shells in cylindrical bending, Compos. Sci. Tech. 29, 169_187, (1987).
Ren J.G., Analysis of simply-supported laminated circular cylindrical shell roofs. Compos. Struct. 11, 277_292, (1989).
Sheng G.G., Wang X., Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Appl. Math. Modelling 34, 2630_2643, (2010).
Soldatos K.P., Hadjigeorgiou V.P., Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels, J. Sound Vib. 137, 369_384, (1990).
Srinivas S., Rao A.K., Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, Int. J. Solids Struct. 6, 1463_1481, (1970).
Vel S.S., Batra R.C., Three-dimensional exact solution for the vibration of functionally graded rectangular plates, J. Sound Vib. 272, 703_730, (2004).
Vel S.S., Mewer R.C., Batra R.C., Analytical solution for the cylindrical bending vibration of piezoelectric composite plates, Int. J. Solids Struct. 41, 1625_1643, (2004).
Vlasov V.Z., The method of initial functions in problems of theory of thick plates and shells, Proc. Ninth Int. Congress Appl. Mech. Brussels, 321_330, (1957).
Wu C.P., Chiu K.H., Thermoelastic buckling of laminated composite conical shells, J. Therm Stresses 24, 881_901, (2001).
Wu C.P., Chen C.W., Elastic buckling of multilayered anisotropic conical shells, J. Aerospace Eng. 14, 29_36, (2001).
Wu C.P., Chiu K.H., Thermally induced dynamic instability of laminated composite conical shells. Int. J. Solids Struct. 39, 3001_3021, (2002).
Wu C.P., Chi Y.W., Three-dimensional nonlinear analysis of laminated cylindrical shells under cylindrical bending. Eur. J. Mech. A/Solids 24, 837_856, (2005).
Wu C.P., Lo J.Y., An asymptotic theory for dynamic responses of laminated piezoelectric shells. Acta Mech. 183, 177_208, (2006).
Wu C.P., Liu K.Y., A state space approach for the analysis of doubly curved functionally graded elastic and piezoelectric shells, Comput. Mater. Continua 6, 177_199, (2007).
Wu C. P., Syu Y.S., Exact solutions of functionally graded piezoelectric shells under cylindrical bending, Int. J. Solids Struct. 44, 6450_6472, (2007).
Wu C.P., Syu Y.S., J.Y. Lo, Three-dimensional solutions for multilayered piezoelectric hollow cylinders by an asymptotic approach, Int. J. Mech. Sci. 49, 669_689, (2007).
Wu C.P., Chiu K.H., Wang Y.M., A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells, Comput. Mater. Continua 18, 93_132, (2008).
Wu C.P., Chiu K.H., Wang Y.M., A mesh-free DRK-based collocation method for the coupled analysis of functionally graded magneto-electro-elastic shells and plates, Comput. Modeling Eng. Sci. 35, 181_214, (2008).
Wu C.P., Chiu K.H., Wang Y.M., A differential reproducing kernel particle method for the analysis of multilayered elastic and piezoelectric plates, Comput. Modeling Eng. Sci. 27, 163_186, (2008).
Wu C.P., Tsai Y.H., Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation, J. Eng. Math. 63, 95_119, (2009).
Wu C.P., Wang J.S., Wang Y.M., A DRK interpolation-based collocation method for the analysis of functionally graded piezoelectric hollow cylinders under electro-mechanical loads, Comput. Modeling Eng. Sci. 52, 1_37, (2009).
Wu C.P., Lu Y.C., A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates, Compos. Struct. 90, 363_372, (2009).
Wu C.P., Li H.Y., The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates, Compos. Struct. 92, 2476_2496, (2010).
Wu C.P., Chiu K.H., Wang Y.M., RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates, Compos. Struct. 93, 923-943, (2010).
Wu C.P., Chen S.J., Chiu K.H., Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method, Mech. Res. Commun. 37, 54_60, (2010).
Ye J.Q., Soldatos K.P., Three-dimensional stress analysis of orthotropic and cross-ply laminated hollow cylinders and cylindrical panels, Comput. Methods Appl. Mech. Eng. 117, 331_351, (1994).
Ye J.Q., Soldatos K.P., Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up, Compos. Eng. 4, 429_444, (1994).
Ye J.Q., Soldatos K.P., Three-dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels, Int. J. Solids Struct. 32, 1949_1962, (1995).
Ye J.Q., Laminated Composite Plates and Shells, Springer-Verlag, London, Great Britain, (2003).