[[alternative]]Transient response of an interface crack subjected to dynamic anti-plane concentrated loading in piezoelectric bimaterials

碩士[[abstract]]本文研究內含電極邊界之界面裂紋的壓電複合材料動力破壞問題，解析一半無限長界面裂紋之六角雙異質壓電材料複合層版，於裂紋面上施載反平面動力點載荷之暫態效應，本文使用積分轉換法與Wiener-Hopf技巧推導壓電材料於拉普拉斯轉換域中之解，接著使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的全場暫態解析解，並求出應力強度因子與電位移強度因子等解析解。最後，將針對應力與電位移之暫態解做數值計算與討論。[[abstract]]In this study, the transient response of a semi-infinite interface crack between two dissimilar piezoelectric materials with the electrode boundary condition is investigated. The useful fundamental solutions are derived and the solutions can be determined by superposition of the fundamental solutions in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in Laplace transform domain) on the interface crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient Full-Field solution and exact transient solution of intensity factors to the problem with concentrated loads are derived. Finally, numerical results are evaluated and discussed in detail.[[tableofcontents]]目錄 目錄........................................................I 圖表目錄................................................III 附錄.....................................................IV 第一章 緒論........................................................1 1.1研究動機........................................................1 1.2文獻回顧...............................................3 1.3內容簡介...............................................6 第二章 理論基礎 2.1線性壓電控制與本構方程式.............................7 2.2拉普拉斯轉換與Cagniard-de Hoop method...............14 2.2.1拉普拉斯轉換（Laplace Transform）.............14 2.2.2 Cagniard-de Hoop method......................15 2.3含靜止裂紋之雙異質壓電材料受反平面應力型負載基本解..15 2.4存在MT表面波 有實根之理論解析.......................26 2.5無MT表面波 無實根之理論解析...........................33 第三章 界面裂紋受反平面動力點載荷之暫態解析..............40 3.1問題描述............................................40 3.2 存在MT表面波之時域解...............................41 3.3 無MT表面波之時域解.................................58 第四章 數值計算與討論...................................72 第五章 成果與討論........................................75 5.1 本文結論...........................................75 5.2本文成果............................................76 5.3尚待研究方向........................................76 參考文獻.................................................78 圖表目錄 圖3-1 界面裂紋之問題描述.................................83 圖3-2 逆轉換路徑圖有剪力頭前波..........................84 圖3-3 逆轉換路徑圖無剪力頭前波..........................85 圖3-4 逆轉換路徑圖有剪力頭前波..........................86 圖3-5 逆轉換路徑圖無剪力頭前波..........................87 圖3-6 之雙異質壓電材料裂紋面施加動力點載荷波前圖.......88 圖3-7 時，有MT表面波圍線積分路徑圖......................89 圖3-8 時，有MT表面波圍線積分路徑圖......................90 圖3-9 時，無MT表面波圍線積分路徑圖......................91 圖3-10 時無MT表面波圍線積分路徑圖.......................92 表4.1壓電材料常數表......................................93 圖4-1a 積分路徑圖.......................................94 圖4-1b 積分路徑圖.......................................95 圖4-2受應力負載含界面裂紋ZnO與PZT4的應力強度因子.........96 圖4-3受應力負載含界面裂紋ZnO與PZT4的電位移強度因子.......97 圖4-4受應力負載含界面裂紋虛擬材料與PZT4的應力強度因子....98 圖4-5受應力負載含界面裂紋虛擬材料與PZT4的電位移強度因子..99 圖4-6數值積分示意圖.....................................100 附錄 附錄一..................................................101[[note]]學號: 695430750, 學年度: 9