功能梯度磁電彈薄層材料之全場理論解析與映射力的探討

Theoretical Analytical Full-field Solutions and Image Forces of Homogeneous and Functionally Graded Magnetoelectroelastic Layered Half-plane

李瑞木(Jui-Mu Lee)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/博士(2008年)

https://doi.org/10.6342/NTU.2008.00620

摘要

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。
一般而言，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。

關鍵字

功能梯度磁電彈材料 ； 映射力

並列摘要

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.
In 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.

並列關鍵字

Functionally graded magnetoelectroelastic material ； Image Forces

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