關於磁電彈材料在工程方面的應用與發展，堆疊式的複合層狀結構是近年來發展的趨勢。 本文的研究主要是以橫向等向性磁電彈材料之線性本構方程式為基礎，理論解析具有力學、電場和磁場耦合之薄層材料域內承受廣義集中力與廣義差排的二維問題。文中利用傅立葉積分轉換技巧與級數展開方法，再導入邊界條件、連續條件與跳躍條件，即可求解出具有映射法物理意義的全場磁電彈薄層解析解。另一方面，對於材料內部的差排所承受的映射力與幾何結構及磁電彈材料特性之關係有完整的分析與探討。藉由瞭解差排映射力的分佈特質，即可推測差排移動的方向與堆積的位置，並可提昇此智慧型磁電彈材料的安全與可靠性。般而言，應力集中的現象經常出現在不同材料特性的均質層狀結構介面處。為了避免材料結構破損，因此，材料特性可隨空間分佈連續變化的功能梯度材料在近幾年中已開始進行大量的研究，而其本身亦可被視為非均質材料。由於功能梯度材料之材料係數是以空間座標的函數表示，所以其分析問題的步驟會較均質材料來的複雜及困難。然而，此功能梯度材料之最大的優點:當材料係數在結構介面處是相同，則所有物理量將會沿著材料幾何介面連續變化，如此將可減少材料的破損並提升其可靠度，本篇論文將深入解析並探討磁電彈功能性材料的特性與行為。For most engineering applications of magnetoelectroelastic materials, the layered composite structures are preferred in future design concept. In this study, the two-dimensional analytical full-field solutions of a transversely isotropic magnetoelectroelastic layered half-plane subjected to generalized line forces and dislocations are presented. The results show that the complete solutions include Green’s function for originally applied singularities in an infinite medium and the other image singularities which are induced to satisfy boundary and interface conditions. The physical meaning of the solution is the image method. With the aid of the generalized Peach-Koehler formula, the explicit expressions of image forces exerted on dislocations are easily derived from the full-field solutions of the generalized stresses.n order to reduce the stress concentration at the interface in laminated structures, the functionally graded materials with continuous material property are developed in recent decade. The magnetoelectroelastic behavior of nonhomogeneous medium is becoming more complicated than that of homogeneous material. However, the physical field quantities along the interface for nonhomogeneous material are more continuous than those for homogeneous material if the material constants at the interface are continuous. A detail investigation and discussion of functionally graded magnetoelectroelastic solid is presented.Abstract Iontents IIIist of Figures VIIIist of Symbols XXVhapter 1 Introduction 1-1 Research Motivation 1-2 Literature Survey 2-2.1 Magnetoelectroelastic solids 2-2.2 Two-dimensional Magnetoelectroelastic Problems 4-2.3 Functionally Graded Magnetoelectroelastic Materials 9-3 Thesis Organization 11hapter 2 Linear Magnetoelectroelasticity 13-1 Constitutive Equations 13-2 Two-dimensional Antiplane Deformation 16-3 Two-dimensional In-plane Deformation 19hapter 3 Analytical Full-field Solutions and Image Forces of Screw Dislocations in a Magnetoelectroelastic Layered Half-plane 23-1 Basic Equations and General Solutions 23-2 Green’s Function of a Magnetoelectroelastic Infinite Plane 26-3 Green’s Function of a Magnetoelectroelastic Layered Half-plane 29-3.1 The Applied Loadings in the Thin Layer 30-3.2 The Applied Loadings in the Half-plane 37-4 Image Forces Exerted on Generalized Screw Dislocations in a Magnetoelectroelastic Layered Half-plane 40-5 Numerical Results and Discussions 45-6 Concluding Remarks 50hapter 4 Image Singularities of Planar Magnetoelectroelastic Bimaterials for Generalized Line Forces and Edge Dislocations 75-1 Basic Equations and General Solutions 75-1.1 Governing Equations 75-1.2 Representation of General Solution 78-1.3 Properties of Roots for the Characteristic Equation 81-2 Exact Full-field Solutions for Magnetoelectroelastic Bimaterials 84-3 The Analysis of Image Singularities for Magnetoelectroelastic Bimaterials 89.3.1 The Locations and Magnitudes of Image Singularities 89.3.2 The Number and Distribution of Image Singularities 94-4 Image Forces Exerted on Generalized Edge Dislocations in Magnetoelectroelastic Bimaterials 95-4.1 Image Forces Exerted on a Single Generalized Dislocation 96-4.2 Image Forces for Two Generalized Dislocations 97-4.3 Image Forces for an Array of Dislocations with Uniform Spacing 98-5 Numerical Results and Discussions 99-6 Concluding Remarks 102hapter 5 Theoretical Analysis of Generalized Loadings and Image Forces in a Planar Magnetoelectroelastic Layered Half-plane 121-1 Analytical Full-field Solutions for a Planar Magnetoelectroelastic Layered Half-plane 121-1.1 The Applied Loadings in the Thin Layer 123-1.2 The Applied Loadings in the Half-plane 130-2 Image Forces Exerted on Generalized Edge Dislocations in a Planar Magnetoelectroelastic Layered Half-plane 134-3 Numerical Results and Discussions 138-4 Concluding Remarks 141hapter 6 Analytical Solutions for Antiplane Problems in Functionally Graded Magnetoelectroelastic Solids 153-1 Formulations and Governing Equations 153-2 Green’s Functions of two Dissimilar Functionally Graded Magnetoelectroelastic Half-planes 157-3 The Characteristics of Magnetoelectroelastic Fields at the Interface for Continuous Material Constants in the Nonhomogeneous Bimaterial 161-4 Green’s Functions of a Functionally Graded Magnetoelectroelastic Layered Half-plane…. 166-4.1 The Applied Loadings in the Thin Layer 166-4.2 The Applied Loadings in the Half-plane 171-5 The Characteristics of Magnetoelectroelastic Fields at the Interface for Continuous Material Constants in the Nonhomogeneous Layered Half-plane 176-6 Numerical Results and Discussions 181-7 Concluding Remarks 186hapter 7 Analytical Solutions for Planar Problems in Functionally Graded Magnetoelectroelastic Solids 212-1 Basic Equations and General Solutions 212-1.1 Governing Equations 212-1.2 Properties of Roots for the Characteristic Equation 218-1.3 Representation of General Solution 221-2 Green’s Functions of Two Dissimilar Planar Functionally Graded Magnetoelectroelastic Half-planes 224-3 The Characteristics of Magnetoelectroelastic Fields at the Interface for Continuous Material Constants 227-4 Green’s Functions of a Functionally Graded Magnetoelectroelastic Layered Half-plane…. 231-4.1 The Applied Loadings in the Thin Layer 231-4.2 The Applied Loadings in the Half-plane 236-5 Numerical Results and Discussions 241-6 Concluding Remarks 243hapter 8 Conclusion and Future Works 252-1 Conclusion 252-2 Future Works 253eferences 255ppendix A 266ppendix B 267ppendix C 269ppendix D 274ppendix E 276ublication List 27
