本文主要討論磁電彈材料的三維和二維材料組成律，當有熱效應時，磁電彈材料的基本方程式，以及使用邊界元素法計算磁電彈材料之二維受熱問題。首先從彈性材料之受熱問題設計邊界元素法著手，之後再藉由史磋公式的便利性，將彈性材料利用矩陣維度的擴張，將其擴充為磁電彈材料，並編寫至師門程式AEPH中，平板因熱效應而產生的應力、應變以及電與磁之變化，主要關注在平板內材料不連續和容易發生疲勞或破壞的地方，目前可處理的問題有孔洞、裂縫等問題。
之後藉由編寫在師門軟體AEPH中的解析解以及商業軟體ANSYS來進行比較，驗證本文的正確性。

This paper discusses the design of BEM for two dimensional magneto-electro-elastic materials under thermal loading. First, we design the codes of Boundary Element Method for two dimensional elastic materials under thermal loading. And then we use the convenience of Stroh formalism to extend the dimension of matrices to complete the solution of the problems of thermo-elasticity for two dimensional magneto-electro-elastic materials. We extend the computer program of our research group AEPH. Furthermore, in order to be sure that the results are correct, the results of Boundary Element Method of AEPH are compared with the ones of analytical solution of AEPH and commercial finite element software ANSYS.

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