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研究生：	蔡宜樺 Tsai, Yi-Hwa
論文名稱：	功能性電磁彈性材料殼結構之三維靜動態行為分析 Three-Dimensional Static and Dynamic Analyses of Functionally Graded Magneto-Electro-Elastic Shells
指導教授：	吳致平 Wu, Chih-Ping
學位類別：	博士 Doctor
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	202
中文關鍵詞：	三維電磁彈性力學、智慧型材料、耦合古典殼理論、微擾法、三維理論、自由振動、動態分析、靜態分析、功能性材料
外文關鍵詞：	Static; Dynamic, Vibration, 3-D theory, Coupled CST, 3-D Magneto-electro-elasticity; Intelligent mate, Perturbation method
相關次數：	點閱：129 下載：3
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本文依據三維電磁彈性力學理論，藉由微擾法推導出功能性電磁彈性材料板殼結構之三維靜動態漸近解析理論。在此三維靜動態漸近解析理論中，根據不同的曲面荷重條件(開放型迴路及封閉型迴路)，分別發展出兩組相應其物理問題之解析模式。首先，本文使用直接消去法，將29條基本電磁彈耦合方程式，化簡成由10個電磁彈性場中的主要變數所表示的微分方程式。透過無因次化、漸近展開及連續積分之求解程序，可將本三維問題分解為具耦合古典殼理論型式(CCST)的二維問題之遞迴控制方程式。動態問題解析中，引入多重時間尺度以消除不同階數問題之長期效應，並使主要場量變數之漸近展開具一致性及可行性。同時，推衍出不同階數的可解條件及歸一正交條件，使本漸近理論之首階解與高階解得以唯一。當應力平衡方程式中，忽略慣性項且假設所有場量變數均與時間變數無關，則運動方程式可簡化成靜態問題之控制方程式。靜態問題解析中，對於開放型迴路及封閉型迴路，則分別考慮三種表面側向荷重。依據本文之三維漸近理論，便可經由一套系統化且具遞迴特性之解析程序，求解各階具CCST型式之控制方程式，以獲得靜動態問題之三維解析解。為求一般性，本文在厚度方向之材料變化，係由考慮為異向性假設出發，進而在單層材料、多層材料及功能性材料中，分別簡化為常數、分層常數及遵循羃次型(或指數型)函數變化。本文藉由許多文獻上提供之標準驗證範例的比較，以驗證三維漸近解析理論在功能性電磁彈性材料板之靜動態問題解析的精確性與收斂性。最後，本文提出功能性電磁彈性材料殼之靜動態問題的數值範例，同時對電磁彈耦合效應及材料變化指數在靜動態問題之特性上，進行一系列之參數研究。

Based on the three-dimensional (3-D) magneto-electro-elasticity, we present two asymptotic formulations for the static and dynamic problems of simply supported, doubly curved, functionally graded (FG) magneto-electro-elastic shells with open-circuit and close-circuit surface conditions using the method of perturbation, respectively. By means of direct elimination, we firstly reduce 29 basic equations of 3-D magneto-electro-elasticity to 10 differential equations in terms of 10 primary variables of magnetic, electric and elastic fields. After performing through the complicated but straightforward derivation such as non-dimensionalization, asymptotic expansion, and successive integration, we finally decompose the present 3-D problem as recursive sets of two-dimensional (2-D) problems with motion equations of the coupled classical shell theory (CCST). The method of multiple time scales is introduced to eliminate the secular terms in various order problems of the present formulation so that the present asymptotic expansion to the primary field variables leads to be uniform and feasible. Both the solvability and orthonormality conditions are derived for the various order problems to uniquely determine the asymptotic solutions of various orders. As the stress equilibrium equations are regardless of the inertial terms and the field varialbes are independent upon the time variables, present motion equations can be reduced to static governing equations. Three different types of loadings applied on the lateral surfaces of the shells with open-circuit and closed-circuit surface conditions are considered in static problems, respectively. Depending on present solution procedure, it is shown that the 3-D asymptotic solutions can be obtained by repeatedly solving the CCST-type governing equations order-by-order in a systematic and hierarchic manner. For the purpose of generality, the material properties in the present asymptotic formulations are regarded to be heterogeneous through the thickness coordinate. Afterwards, they are further specified to be constants in single-layer shells, to be layerwise constants in multilayered shells and to obey an identical power-law (or exponent-law) distribution in FG shells. The present asymptotic formulations are simultaneously applied to several benchmark problems to validate the accuracy and the rate of convergence of present asymptotic solutions. Parametric studies for both the coupled magneto-electro-elastic effect and the influence of material property gradient index on static and dynamic characteristics of FG magneto-electro-elastic shells are studied.

Abstract..................................................I
Abstract (in Chinese)………………………………………………II
Acknowledgements (in Chinese)………………………………...III
Contents…………………………………………………………………V
List of Tables………………………………………………………IX
List of Figures………………………………………….........XII
Nomenclature………………………………………………………..XV 
Chapter 1	Introduction………………………………………….....1
1.1	Background and Literature Review…………….......1
1.2	Overview of Present Thesis…………………………...8
Chapter 2	Dynamic Responses of Magneto-Electro-Elastic Shells………...............11
2.1	Basic Motion Equations of 3-D Magneto-Electro-Elasticity…………………….11
2.2 	Non-dimensionalization……………………………....14
2.3	Asymptotic Expansions………………………………...17
2.3.1	Open-Circuit Surface Conditions (j = 0)…….....17
2.3.2 Closed-Circuit Surface Conditions (j = 2)………....19
2.4	Successive Integration………………………........21
2.4.1  Open-Circuit Surface Conditions (j = 0)…….......21
2.4.2	Closed-Circuit Surface Conditions (j = 2)……….26
Chapter 3	Static Behaviors of Magneto-Electro-Elastic Shells……………..........31
3.1	Basic Static Equations of 3-D Magneto-Electro-Elasticity…………………..31
3.2	Asymptotic Expansions………………………………...33
3.2.1	Open-Circuit Surface Conditions (j = 0)………...33
3.2.2	Closed-Circuit Surface Conditions (j = 2)……...34
3.3	Successive Integration…………………………………36
3.3.1	Open-Circuit Surface Conditions (j = 0)………….36
3.3.2	Closed-Circuit Surface Conditions (j = 2)……...39
Chapter 4		Cylindrical Bending Vibrations of Piezoelectric Shells……..43
4.1	Basic Motion Equations of 3-D Piezoelectricity…43
4.2	Asymptotic Expansions…………………………….....46
4.2.1	Open-Circuit Surface Conditions (j = 0)………...46
4.2.2	Closed-Circuit Surface Conditions (j = 2)……...49
4.3	Successive Integration…………………………………51
4.3.1	Open-Circuit Surface Conditions (j = 0)………….51
4.3.2	Closed-Circuit Surface Conditions (j = 2)……...56
Chapter 5	Applications to Benchmark Problems…………......61
5.1	Dynamic Responses of Magneto-Electro-Elastic Shells……...............61
5.1.1	Open-Circuit Surface Conditions (j = 0)………….61
5.1.2	Closed-Circuit Surface Conditions (j = 2)……...66
5.2	Static Behaviors of Magneto-Electro-Elastic shells……………………….70
5.2.1	Open-Circuit Surface Conditions (j = 0)………...70
5.2.2	Closed-Circuit Surface Conditions (j = 2)……...72
5.3	Cylindrical Bending Vibrations of Piezoelectric Shells…………….........74
5.3.1	Open-Circuit Surface Conditions (j = 0)………….74
5.3.2 	Closed-Circuit Surface Conditions (j = 2)……...78
Chapter 6	Illustrative Examples…………………………….....82
6.1	Dynamic Responses of Magneto-Electro-Elasticity….............83
6.1.1	Functionally Graded Elastic Plates…………………83
6.1.2	Functionally Graded Piezoelectric Plates…………85
6.1.3	Multilayered Magneto-Electro-Elastic Plates…….86
6.1.4	Functionally Graded Magneto-Electro-Elastic Plates……………………….87
6.1.5	Functionally Graded Magneto-Electro-Elastic Shell....................88
6.2	Static Behaviors of Magneto-Electro-Elasticity..90
6.2.1	Single-layer Piezoelectric Flat-Panels………....91
6.2.2	Multilayered Magneto-Electro-Elastic Plates…….92
6.2.3	Multilayered Magneto-Electro-Elastic Shells…….93
6.2.4	Functionally Graded Magneto-Electro-Elastic Shell...................96
6.3	Cylindrical Bending Vibrations of Piezoelectricity........98
6.3.1	Functionally Graded Elastic Plates…………………98
6.3.2	Multilayered Piezoelectric Plates………………...99
6.3.3	Functionally Graded Piezoelectric Plates……….100
6.3.4	Functionally Graded Piezoelectric Shells……….101
Chapter 7	Conclusions and Recommendations…………………..103
References………………….…………………..105
Tables………………………………..………….115
Figures…………………..……………………..155
Appendix	A……………………………………...189
Appendix	B………………………………….....192
Appendix C……………………………………...196
Appendix D……………………………………….198
Appendix	E…………………..………………...200
Vita (in Chinese)…………………..……………………201
                                    

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