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系統識別號 U0026-1707202014411200
論文名稱(中文) 複變理論退化性材料之數值分析
論文名稱(英文) Numerical Analysis for Degenerate Materials on Complex Variable Formalism
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 108
學期 2
出版年 109
研究生(中文) 陳潔妤
研究生(英文) Chieh-Yu Chen
學號 P46074202
學位類別 碩士
語文別 中文
論文頁數 82頁
口試委員 指導教授-胡潛濱
口試委員-楊文彬
口試委員-夏育群
中文關鍵字 史磋公式  異向性彈性力學  退化性材料  壓電材料  磁電彈材料 
英文關鍵字 Stroh formalism  Anisotropic elasticity  degenerate material  piezoelectric material  magneto-electro-elastic material 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 摘要 I
Abstract II
致謝 VI
目錄 VII
表目錄 IX
圖目錄 X
符號說明 XII
第一章 緒論 1
1.1研究目的 1
1.2文獻回顧 1
1.3本文架構 2
第二章 史磋公式 3
2.1異向性彈性材料 3
2.2壓電材料 3
2.3磁電彈材料 4
2.4通解 5
2.5重根修正解 7
第三章 退化性材料 9
3.1退化性材料介紹 9
3.2基本彈性矩陣之分類 11
3.3退化性材料 12
3.3.1第一類退化性基本彈性矩陣 13
3.3.2第二類退化性基本彈性矩陣 14
3.3.3特殊退化性基本彈性矩陣 14
3.3.4彈性勁度矩陣及彈性柔度矩陣 15
3.4虛擬退化性材料 16
3.4.1第一類退化性材料 16
3.4.2第二類退化性材料 24
3.4.3特殊退化性材料 32
3.5異類材料之結合 36
第四章 微擾技巧 38
4.1退化性材料之微擾 38
4.1.1退化性材料微擾方式 38
4.1.2退化性材料微擾驗證 41
4.2異類材料之微擾 47
4.2.1異類材料微擾設定 47
4.2.2異類材料微擾驗證 49
第五章 實例驗證 52
5.1退化性材料 52
5.2異類材料 67
第六章 結論 76
參考資料 77
附錄A 微擾值ε之選取 80
附錄B 多次微擾 82
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