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研究生:陳威任
研究生(外文):Wei-RenChen
論文名稱:含異向性彈性/壓電/磁電彈異質之應力分析
論文名稱(外文):Stress Analysis of Inclusion with Anisotropic Elastic, Piezoelectric, and/or Magneto-Electro-Elastic Materials
指導教授:胡潛濱
指導教授(外文):Chyan-bin Hwu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:67
中文關鍵詞:史磋公式異向性彈性力學異質壓電材料壓磁材料磁電彈材料
外文關鍵詞:Stroh formalismanisotropic elasticityinclusionpiezoelectric materialmagneto-electro-elastic material
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二維異向性彈性力學的史磋公式(Stroh formalism)可以藉由擴張相關矩陣維度大小而延伸應用到壓電材料及磁電彈材料,由於多數文獻僅探討單一種材料相關孔洞、裂縫或異質等平板問題,本文利用此特性,提出一種矩陣調適法來處理同時含有異向性彈性材料、壓電材料、壓磁材料及磁電彈材料的異質問題。利用此方式,在文獻中針對異向性彈性材料異質問題推導出的解析解、邊界元素法及邊界有限元素法皆不須重新推導,即可直接應用在多種材料同時使用的異質問題,並融入本師門研究團隊所編寫的結構分析軟體(Anisotropic Elastic Plate_Hwu, AEPH)。
最後設計三種問題來探討異質與基材交界處的應力集中因子、電位移、磁通量及裂縫的應力強度因子,包括:(1)壓磁材料板含有一個異向性彈性材料或壓電材料異質、(2)壓磁材料板含有一個異向性彈性材料或壓電材料異質和一個裂縫、(3)壓磁材料或磁電彈材料板含有兩個異向性彈性材料或壓電材料異質,並經由與其他解析解和有限元素軟體ANSYS進行比對證明本方式的可行性及正確性。此調整方式亦可應用在其他多材料問題之分析及實際應用。
Based upon the special feature that Stroh formalism for two-dimensional anisotropic elasticity can be extended to the piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension, an adaptable adjustment technique is proposed to deal with the problems with simultaneous existence of anisotropic, piezoelectric and magneto-electro-elastic materials. With this technique, the analytical solutions, boundary element methods and boundary-based finite element method developed previously for the problems of anisotropic elastic inclusion can now be employed to most of the related inclusion problems with simultaneous existence of these three different kinds of materials. This technique also be applied to AEPH, the structure engineering analysis software of our group. To verify the correctness of the proposed method, three typical examples: (1) one anisotropic/piezoelectric inclusion in piezomagnetic matrix, (2) one anisotropic/piezoelectric inclusion and one crack in piezomagnetic matrix, (3) two anisotropic/piezoelectric inclusions in piezomagnetic/magneto-electro-elastic matrix, are presented and compared with the other existing solutions. This technique also can be applied to analysis of other multi-material problems and some practical applications.
摘要----------------------------------------------------------------I
Abstract-------------------------------------------------------------II
誌謝---------------------------------------------------------------IX
目錄---------------------------------------------------------------X
表目錄-----------------------------------------------------------XIII
圖目錄-----------------------------------------------------------XIV
符號--------------------------------------------------------------XV
第一章 緒論---------------------------------------------------------1
1.1 文獻回顧----------------------------------------------------1
1.2 研究目的----------------------------------------------------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
第三章 矩陣調適法---------------------------------------------------7
3.1 調整步驟----------------------------------------------------8
第四章 異質問題----------------------------------------------------11
4.1 均佈力施加在無限遠處---------------------------------------12
4.2 點力施加在異質外部-----------------------------------------13
4.3 差排施加在異質外部-----------------------------------------15
4.4 異質與裂縫之交互作用---------------------------------------16
第五章 邊界元素分析------------------------------------------------19
5.1 邊界積分方程式---------------------------------------------19
5.2 特殊邊界元素法---------------------------------------------22
5.3 邊界有限元素法---------------------------------------------22
第六章 AEPH程式設計----------------------------------------------25
6.1控制變數及輸入檔案------------------------------------------25
6.2 架構與計算流程---------------------------------------------30
第七章 數值範例----------------------------------------------------34
7.1壓磁基材含單一異向性彈性或壓電異質--------------------------36
7.2壓磁基材含單一異向性彈性或壓電異質及一裂縫------------------38
7.3壓磁或磁電彈基材含兩個異向性彈性或壓電異質------------------41
第八章 結論--------------------------------------------------------45
參考文獻-----------------------------------------------------------46
附錄A 微小值 k 之選取---------------------------------------------51
附錄B 映射點之選取------------------------------------------------52
附錄C 點力及差排之解析解修正--------------------------------------59
附錄D AEPH異質與裂縫距離相關問題---------------------------------65
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