臺灣博碩士論文加值系統

本文以改良 Pagano 方法探討一簡支承、功能性梯度焦電彈材料中空多層疊合圓柱殼在溫度載重作用下的三維耦合行為。文中考慮四種不同的側向邊界條件，且功能性材料殼的材料性質沿著厚度方向為非均質，且依指數律分佈。以往Pagano 方法多用來分析多層疊合複合材料殼、板，經過改良後可用來分析功能性梯度焦電彈材料多層疊合圓柱殼。改良之處包括：以Reissner混合變分原理替代以位移為主變數之虛位移原理、將系統方程式的複數型解轉換成對應的實數型解、採用連續近似法與發展傳遞矩陣法使其能夠適用於功能性材料殼的熱傳導分析和焦電彈耦合分析。本文亦探討材料梯度指標、半徑－厚度比和各層間的厚度比等各參數的變異對耦合行為中各場量變數的影響。

A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezo-thermo-elastic material (FGPM) circular hollow sandwich cylinders under thermal loads, in which four different surface conditions are considered. The material properties of each individual layer, constituting the cylinders, are regarded as heterogeneous through the thickness coordinate in this formulation, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of laminated composite plates and shells, is modified to be feasible for the study of FGPM sandwich cylinders. The modifications include that 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 introduced in this analysis, and a propagator matrix method is developed and applied for the heat conduction and coupled piezo-thermo-elastic analyses of the FGPM sandwich cylinders. A parametric study of the influence of the radius-to-thickness ratio, thickness ratio for each layer, surface conditions, and material-property gradient index on assorted field variables, induced in the FGPM sandwich cylinders, is undertaken.

中文摘要 .......................................................... I
英文摘要 .......................................................... II
誌謝 ............................................................. III
目錄 ............................................................. IV
表目錄 ........................................................... VI
圖目錄 .......................................................... VII
第一章 緒論...................................................... 1
第二章 三維焦電彈力學基本方程式 ................................. 7
2.1 基本方程式 .................................................. 7
2.2 無因次化 ................................................... 10
第三章 改良Pagano 法 ........................................... 15
3.1 雙傅立葉級數展開法 ......................................... 15
3.2 齊性與非齊性線性方程組理論 ................................. 16
3.2.1 齊性線性方程系統 ....................................... 16
3.2.2 非齊性線性方程系統 ..................................... 18
3.3 連續近似法 ................................................. 18
3.4 傳遞矩陣法 ................................................. 20
3.4.1 熱傳導分析.............................................. 21
3.4.2 焦電彈耦合分析 ......................................... 22
第四章 數值範例 ................................................ 24
4.1 單層之均質焦電彈材料圓柱殼 ................................. 24
4.2 多層疊合焦電彈材料圓柱殼 ................................... 25
4.3 多層疊合功能性梯度焦電彈材料圓柱殼 ........................ 27
第五章 結論..................................................... 30
參考文獻 ......................................................... 31
表 ............................................................... 36
圖 ............................................................... 41
附錄 A .......................................................... 49
附錄 B .......................................................... 50
自述 ............................................................. 51

Ashida, F. and Tauchert, T.R. 2000. “Plane Stress Problem of a Piezothermoelastic Plate, Acta Mech., 145: 127_134.
Bansal, A. and Ramaswamy, A. 2002. “FE Analysis of Piezo-Laminate Composites under Thermal Loads, J. Intell. Mater. Sys. Struct., 13:291_301.
Dai, H.L., Hong, L., Fu, Y.M. and Xiao, X. 2010. “Analytical Solution for Electromagnetothermoelastic Behaviors of a Functionally Graded Piezoelectric Hollow Cylinder, Appl. Math. Modeling, 34: 343_357.
Dai, H.L. and Wang, X. 2006. “Magneto-Thermo-Electro-Elastic Transient Response in a Piezoelectric Hollow Cylinder Subjected to Complex Loadings, Int. J. Solids Struct., 43:5628_5646.
Dube, G.P., Kapuria, S. and Dumir, P.C. 1996a. “Exact Piezothermoelastic Solution of Simply-Supported Orthotropic Flat Panel in Cylindrical Bending, Int. J. Mech. Sci., 38:1161_1177.
Dube, G.P., Kapuria, S. and Dumir, P.C. 1996b. “Exact Piezothermoelastic Solution of Simply-Supported Orthotropic Circular Cylindrical Panel in Cylindrical Bending, Arch. Appl. Mech., 66:537_554.
Dube, G.P., Upadhyay M.M., Dumir, P.C. and Kumar, S. 1998. “Piezothermoelastic Solution for Angle-Ply Laminated Plate in Cylindrical Bending, Struct. Eng. Mech., 6:529_542.
Dumir, P.C., Dube, G.P. and Kumar, S. 1997. “Piezothermoelastic Solution for Angle-Ply Laminated Cylindrical Panel, J. Intell. Mater. Sys. Struct., 8:452_464.
Dumir, P.C., Kumari, P. and Kapuria, S. 2009. “Assessment of Third Order Smeared and Zigzag Theories for Buckling and Vibration of Flat Angle-Ply Hybrid Piezoelectric Panels, Compos. Struct., 90:346_362.
Jonnalagadda, K.D., Blandford, G.E. and Tauchert, T.R. 1994. “Piezothermoelastic Composite Plate Analysis Using First-Order Shear Deformation Theory, Comput. Struct., 51:79_89.
Kapuria, S. and Achary, G.G.S. 2006. “Electromechanically Coupled Zigzag Third-Order Theory for Thermally Loaded Hybrid Piezoelectric Plates, AIAA J., 44:160_170.
Kapuria, S. and Achary, G.G.S. 2008. “Benchmark 3D solution and Assessment of A Zigzag Theory for Free Vibration of Hybrid Plates under Initial Electrothermomechanical Stresses, Compos. Sci Technol., 68:297_311.
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.
Kapuria, S., Dumir, P.C. and Sengupta, S. 1997. “Exact Axisymmetric Solution for a Simply Supported Piezoelectric Cylindrical Shell, Arch. Appl. Mech., 67:260_273.
Kapuria, S., Sengupta, S. and Dumir, P.C. 1997. “Three-Dimensional Solution for a Hybrid Cylindrical Shell under Axisymmetric Thermoelectric Load, Arch. Appl. Mech., 67:320_330.
Ootao, Y. 2009. “Transient Thermoelastic and Piezothermoelastic Problems of Functionally Graded Materials, J. Therm. Stresses, 32:656_697.
Ootao, Y., Akai, T. and Tanigawa, Y. 2008. “Transient Piezothermoelastic Analysis for a Functionally Graded Thermopiezoelectric Hollow Cylinder, J. Therm. Stresses, 31:935_955.
Ootao, Y. and Tanigawa, Y. 2007. “Transient Piezothermoelastic Analysis for a Functionally Graded Thermopiezoelectric Hollow Sphere, Compos. Struct., 81:540_549.
Soldatos, K.P. and Hadjigeorgiou, V.P. 1990. “Three-Dimensional Solution of the Free Vibration Problem of Homogeneous Isotropic Cylindrical Shells and Panels, J. Sound Vib., 137:369-384.
Tang, Y.Y., Noor, A.K. and Xu, K. 1996. “Assessment of Computational Models for Thermoelectroelastic Multilayered Plates, Comput. Struct., 61:915_933.
Tauchert, T.R.., Ashida, F., Noda, N., Adali, S. and Verijenko, V. 2000. “Developmemts in Thermopiezoelasticity with Relevance to Smart Composite Structures, Compos. Struct., 48:31_38.
Wu, C.P., Chen, S.J. and Chiu, K.H. 2010. “Three-Dimensional Static Behavior of Functionally Graded Magneto-Electro-Elastic Plates Using the Modified Pagano Method, Mech. Res. Commun., 37:54_60.
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., 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, Comput. Mater. Continua, 8:93_132.
Wu, C.P., Lu, Y.C. 2009. “A Modified Pagano Method for the 3D Dynamic Responses of Functionally Graded Magneto-Electro-Elastic Plates, Compos. Struct., 90:363_372.
Wu, C.P., Syu, Y.S. and Lo, J.Y. 2007. “Three-Dimensional Solutions for Multilayered Piezoelectric Hollow Cylinders by an Asymptotic Approach, Int. J. Mech. Sci., 49:669_689.
Wu, X.H., Shen, Y.P. and Chen, C. 2003. “An Exact Solution for Functionally Graded Piezothermoelastic Cylindrical Shell as Sensors or Actuators, Mater. Letters, 57:3532_3542.
Xiang, H.J. and Shi, Z.F. 2009. “Static Analysis for Functionally Graded Piezoelectric Actuators or Sensors under a Combined Electro-Thermal Load, Eur. J. Mech. A/Solids, 28:338_346.
Xu, K., Noor, A.K. and Tang, Y.Y. 1995. “Three-Dimensional Solutions for Coupled Thermo-Electro-Elastic Response of Multilayered Plates, Comput. Methods Appl. Mech.Eng., 126:355_371.
Zhang, C., Di, S. and Zhang, N. 2002. “A New Procedure for Static Analysis of Thermo-Electric Laminated Composite Plates under Cylindrical Bending, Compos. Struct., 56:131_140.
Zhong, Z. and Shang, E.T. 2005. “Exact Analysis of Simply Supported Functionally Graded Piezothermoelectric Plates, J. Intell. Mater. Syst. Struct., 16: 643_651.