在史磋公式中，一旦碰到基本彈性矩陣(fundamental elasticity matrix)內有重複特徵向量的材料：退化性材料，即會無法使用原本的通解；本文利用數值分析的方式，在材料性質矩陣中加入微擾，在不影響材料性質的情況下，使材料能有各自獨立的特徵向量。而藉由史磋公式，我們能夠利用矩陣維度的擴充，將異向性彈性材料的通解，延伸到壓電材料以及磁電彈材料；於是在異類材料結合的題目中，我們可以將較低維度的材料視為高維度材料的退化性材料，並由調整矩陣維度的方式處理這類問題。最後我們將研究成果寫進師門發展的結構分析軟體AEPH（Anisotropic Elastic Plate_Hwu）中，進而讓程式能夠處理相關的問題。
實例驗證的部份，我們將退化性材料以孔洞、裂縫及異質問題做範例，且列出不加微擾的結果，並以此與微擾後之結果相對比，說明微擾的重要性。而針對異類材料，我們利用典型的異質問題做範例，且分別利用不同維度的材料做比對，以確保適用於各種維度的材料。其中的結果，我們都與有限元素分析軟體ANSYS做驗證，以確保結果之正確性。

The general solution of the Stroh formalism is based upon the assumption that the fundamental elasticity matrix can compute distinct eigenvalues, so that there will be six independent eigenvectors. That means when we use degenerate materials which have only one or two independent eigenvectors, the Stroh formalism does not apply. In numerical calculation, we give degenerate materials a small perturbation which will not affect the material properties and can lead us find the corresponding eigenvectors. Due to the special feature of the Stroh formalism, the analysis of two-dimensional anisotropic elasticity can be extended to the piezoelectric materials and magneto-electro-elastic materials by expanding the related matrix dimension. In the problem with multiple types of materials, we consider the material which has lower dimension as the degenerate material of one has the highest dimension, and we use adaptable adjustment technique to solve it. To verify the correctness of the method we mentioned, the result calculated by the software of our group AEPH will be compare with the finite element software ANSYS.

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