本文根據三維磁電彈性力學理論，藉由微擾法，推導出含磁電彈性材料之中空圓柱層殼之三維漸近解析理論。首先，透過圓柱座標系將三維磁電彈性力學之29條基本方程式重新組合，消去曲面應力場量，並以彈性位移、橫向應力、電位差、磁位差、電位移與磁位移等10個場量為主要變數，將29條基本方程式化簡為10條微分方程式；再藉由適當的無因次化處理，使用漸近展開法，將各場量展開成與一微小參數相關之冪級數型式，則原三維基本方程式可分離成不同階數、層次分明且具遞迴特性之微分方程組。依序將各階微分方程式沿厚度方向進行連續積分，並透過雙傅立葉級數展開，可導出由低階至高階遞迴型式之二維控制方程式，其中，古典殼理論即為此近似理論之首階近似解。利用類似古典殼理論之解析方法可逐階求解，以求得收歛之精確解。文中應用推得之含磁電彈性材料中空圓柱殼之三維漸近理論解，解析兩端為簡支承且受正弦型式分佈外力場、電場或磁場作用下之數值範例，其數值驗證顯示，無論在收斂性和精確度上均有理想之結果。

Exact　solutions　for　multilayered　magneto-electro-elastic　hollow　cylinders　are　presented　on　the　basis　of　three-dimensional (3D)　linear　magneto-electro-elasticity.　The　twenty-nine　basic　equations　are　firstly　reduced　to　ten　differential　equations　in　terms　of　ten　primary　variables　of　elastic,　electric　and　magnetic　fields.　After　going　through　the　mathematical　manipulation　of　nondimensionalization,　asymptotic　expansion and　successive　integration,　we　finally　obtain　recurrent　sets　of　two-dimensional　(2D)　governing　equations　for　various　order　problems.　These　2D　governing　equations　are　merely　those　derived　using　the　assumptions　for　field　variables　in　the　classical　shell　theory　(CST).　Hence,　the　CST-type　governing　equations　are　derived　as　a　first-order　approximation　to　the　3D　magneto-electro-elasticity.　The　leading　order　solutions　and　higher-order　corrections　can　be　determined　by　treating　the　CST-type governing　equations　in　a　systematic　and　consistent　way.　Several　benchmark　solutions　for　multilayered　magneto-electro-elastic　hollow　cylinders　under　mechanical,　electric and　magnetic　loads　are　given　to　demonstrate　the　performance　of　the　theory.

Chandrashekhara, K., Kumar, B.S., 1993. Static analysis of a thick laminated circular cylindrical shell subjected to axisymmetric load. Compos. Struct. 23, 1_9.
Chee, C.Y.K., Tong, L., Steven G.P., 1998. A review on the modeling of piezoelectric sensors and actuators incorporated in intelligent structures. J. Intelligent Mater. Systems and Struct. 9, 3_19.
Cheng, Z.Q., Lim, C.W., Kitipornchai, S., 2000. Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates. Int. J. Solids Struct. 37, 3153_3175.
Gopinathan, S.V., Varadan, V.V., Varadan, V.K., 2000. A review and critique of theories for piezoelectric laminates. Smart Mater. Struct. 9, 24_48.
Heyliger, P., 1994. Static behavior of laminated elastic/piezoelectric plates. AIAA J. 32, 2481_2484.
Heyliger, P., 1997a. Exact solutions for simply supported laminated piezoelectric plates. J. Appl. Mech., ASME, 64, 299_306.
Heyliger, P., 1997b. A note on the static behavior of simply-supported laminated piezoelectric cylinders. Int. J. Solids Struct. 34, 3781_3794.
Kapuria, S., Dumir, P.C., Sengupta, S., 1997. An exact axisymmetric solution for a simply supported piezoelectric cylindrical shell. Archive Applied Mech. 67, 260_273.
Lee, J.S., Jiang, L.Z., 1996. Exact electroelastic analysis of piezoelectric laminae via state space approach. Int. J. Solids Struct. 33, 977_990.
Pan, E., 2001. Exact solution for simply supported and multilayered magneto-electro-elastic plates. J. Appl. Mech. 68, 608_618.
Pan, E., Han, F., 2005. Exact solution for functionally graded and layered magneto-electro-elastic plates. Int. J. Eng. Sci. 43, 321_339.
Pan, E., Heyliger, P.R., 2003. Exact solutions for magneto-electric-elastic laminates in cylindrical bending. Int. J. Solids Struct. 40,6859_6876.
Saravanos, D.A., Heyliger, P.R., 1999. Mechanics and computational models for laminated piezoelectric beams, plates, and shells. Appl. Mech. Rev. 52, 305_319.
Wang, J., Chen, L., Fang, S., 2003. State vector approach to analysis of multilayered magneto-electro-elastic plates. 40, 1669_1680.
Wu, C.P., Chi, Y.W., 2005a. Three-dimensional nonlinear analysis of laminated cylindrical shells under cylindrical bending. Euro. J. Mech. A/Solids 24, 837_856.
Wu, C.P., Chiu, S.J., 2001. Thermoelastic buckling of laminated composite conical shells. J. Therm. Stresses 24, 881_901.
Wu, C.P., Chiu, S.J., 2002. Thermally induced dynamic instability of laminated composite conical shells. Int. J. Solids Struct. 39, 3001_3021.
Wu, C.P., Pu, Y.F., Tsai, Y.H., 2005b. Asymptotic solutions of axisymmetric laminated conical shells. Thin-Walled Struct. 43, 1589_1614.
Wu, C.P., Tarn, J.Q., Chi, S.M., 1996a. Three-dimensional analysis of doubly curved laminated shells. J. Engrg. Mech., ASCE 122, 391_401.
Wu, C.P., Tarn, J.Q., Chi, S.M., 1996b. An asymptotic theory for dynamic response of doubly curved laminated shells. Int. J. Solids Struct. 33, 3813_3841.