在異向性彈性力學的探討上，史磋公式（Stroh Formalism）可以藉由擴充相關材料性質矩陣的維度大小，進而延伸應用至壓電材料，以及磁電彈材料。本文中，利用此特性，則文獻中提及的無限板、孔洞、裂縫和異質問題之解析解，以及邊界元素法基本解皆不須重新推導，在智慧型材料分析中，我們經常以彈性複材板做為基材，以壓電或磁電彈材料作為感測器，因此本文也運用了矩陣的調適法，使得我們可以同時處理包含異向性彈性材料、壓電材料以及磁電彈材料的題目。而在邊界元素振動的探討中，我們一樣可以藉由史磋公式的特性，調整部分矩陣維度以及內容，不須經過重新推導即可直接延用至壓電材料以及磁電彈材料，最後將研究成果融入師門使用MATLAB程式語言撰寫出一套命名為AEPH（Anisotropic Elastic Plate_Hwu）的結構分析軟體中。
為了驗證擴充的正確性，本文分析以下三種狀況，自由振動、穩態振動以及暫態振動的問題。在這些問題中，我們同時也加入了無限板、孔洞、裂縫以及異質振動的相關問題，探討其位移、應力、電場以及磁場與時間的關係，並經由商用有限元素分析軟體 ANSYS 來進行比對，以證明此擴充方式的可行性。

Based upon the special feature of Stroh formalism, the analysis of two-dimensional anisotropic elasticity can be extended to the piezoelectric and magneto-electro-elastic materials (MEE) by expanding the related matrix dimension. By using the adaptable adjustment technique, the structure with simultaneous existence of anisotropic elastic, piezoelectric and magneto-electro-elastic materials can know be solved. With this technique, the analytical solutions, boundary element methods and even the dynamic problem in boundary element methods can now be employed in the problem with multiple kinds of materials. To show the correctness of the expansion in dynamic analysis of boundary element methods in piezoelectric and magneto-electro-elastic materials, three different kinds of analysis is considered. Free vibration, Steady-state vibration and Transient vibration are shown in this paper. Furthermore, the problem of a plate with cracks, inclusions, or holes are also mentioned. To testify the piezoelectric and magneto-electro-elastic dynamic analysis, the result calculated by the structure analysis software of our group AEPH will be compare with the commercial finite element software ANSYS.

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