本文研究主題為含真空邊界靜止裂紋之壓電材料動力破壞問題，解析一含半無限長靜止裂紋之壓電材料，於域內任意處施予一應力型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一次拉普拉斯轉換域中，受空間指數應力與電位移分佈型之基本解，並利用此基本解來解析此包含特徵長度的壓電材料動力破壞問題，文中使用Cagniard-de Hoop方法來作拉普拉斯逆轉換得到時域中的解。最後，本文將針對應力場、應力強度因子與電位移強度因子等解析解，做詳細的數值計算與討論。

In this study, the transient response of a semi-infinite crack subjected to dynamic anti-plane concentrated loading in a hexagonal piezoelectric medium with vacuum boundary conditions is investigated. Two 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 problems are the problems of applying exponentially distributed traction or electric displacements  (in Laplace transform domain) on the crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solutions in time domain. Exact transient Full-Field solutions and exact transient solutions of intensity factors to the problem are both derived. Finally, numerical results are evaluated and discussed in detail.

目錄  ………………………………………………………………… I
圖表目錄  …………………………………………………………… III
第一章	緒論  ………………………………………………………1
1.1	研究動機與文獻回顧  …………………………………1
1.2	研究方法與內容簡介  …………………………………6
第二章	理論基礎與基本解  ………………………………………8
2.1	線彈性壓電控制與本構方程式  ………………………8
2.2	拉普拉斯轉換與Cagniard-de Hoop method  …………9
2.2.1	拉普拉斯轉換  ………………………………………9
2.2.2	Cagniard-de Hoop method  ………………………10
2.3	含真空邊界靜止裂紋之壓電材料受反平面應力型基本解  ………………………………………………11
2.4	含真空邊界靜止裂紋之壓電材料受平面電位移型基本解  ………………………………………………23
2.5	無窮域壓電材料受反平面動力點載荷之全場解  ………………………………………………………29
第三章	含半無限長裂紋之壓電材料受反平面動力點載荷之全場解析  …………………………………………………………37
3.1	問題描述  ……………………………………………37
3.2	上半平面之全場解  ……………………………………37
3.3	下半平面之全場解  ……………………………………60
3.4	強度因子  …………………………………………76
第四章	數值計算與討論  …………………………………………80
4.1	波傳的分析與討論(上半平面)  …………………80
4.2	波傳的分析與討論(下半平面)  …………………83
4.3	強度因子   ……………………………………………86
第五章	結論  ………………………………………………………87
5.1	本文結論  ……………………………………………87
5.2	本文成果  ……………………………………………87
5.3	尚待研究的方向  ……………………………………89
附錄  …………………………………………………………………91
A.	觀察點位於上半平面 全場解  ………………………91
B.	觀察點位於下半平面 全場解  ………………………95
C.	觀察點位於上半平面 與 全場解  …………………99
D.	觀察點位於下半平面 與 全場解  ………………102
E.	電位移暫態圖(上半平面)  ……………………………106
F.	電位移暫態圖(下半平面)  ……………………………112
參考文獻  …………………………………………………………118
 
圖 表 目 錄
圖2.1	 真空基本解的邊界描述  ……………………………………125
圖2.2	 積分路徑  …………………………………………………126
圖2.3	 無窮域基本解的邊界描述  ………………………………127
表3.1	 上半平面之波前統整  …………………………………128
表3.2	 下半平面之波前統整  …………………………………129
圖3.1	 靜止裂紋之問題描述  ………………………………………130
圖3.2.1(a)	情況一：聲波積分路徑圖  ……………………………131
圖3.2.1(b)	情況一：電磁波積分路徑圖  …………………………132
圖3.2.2(a)	情況二：聲波積分路徑圖  ……………………………133
圖3.2.2(b)	情況二：電磁波積分路徑圖  …………………………134
圖3.2.3(a)	情況三：聲波積分路徑圖  ……………………………135
圖3.2.3(b)	情況三： 積分路徑圖  ……………………………136
圖3.2.3(c)	情況三：電磁波積分路徑圖  …………………………137
圖3.2.4(a)	情況四：聲波積分路徑圖  ……………………………138
圖3.2.4(b)	情況四：電磁波積分路徑圖  …………………………139
圖3.2.5(a)	情況五：聲波積分路徑圖  ……………………………140
圖3.2.5(b)	情況五： 積分路徑圖  ……………………………141
圖3.2.5(c)	情況五：電磁波積分路徑圖  …………………………142
圖3.2.6(a)	情況六：聲波積分路徑圖  ……………………………143
圖3.2.6(b)	情況六：電磁波積分路徑圖  …………………………144
圖3.3.1(a)	情況一：聲波積分路徑圖  ……………………………145
圖3.3.1(b)	情況一：電磁波積分路徑圖  …………………………146
圖3.3.2(a)	情況二：聲波積分路徑圖  ……………………………147
圖3.3.2(b)	情況二：電磁波積分路徑圖  …………………………148
圖3.3.3(a)	情況三：聲波積分路徑圖  ……………………………149
圖3.3.3(b)	情況三：電磁波積分路徑圖  …………………………150
圖3.3.4(a)	情況四：聲波積分路徑圖  ……………………………151
圖3.3.4(b)	情況四：電磁波積分路徑圖  …………………………152
圖3.3.5(a)	情況五：聲波積分路徑圖  ……………………………153
圖3.3.5(b)	情況五：電磁波積分路徑圖  …………………………154
圖3.3.6(a)	情況六：聲波積分路徑圖  ……………………………155
圖3.3.6(b)	情況六：電磁波積分路徑圖  …………………………156
圖3.4	  積分路徑圖  ………………………………………………157
表4.1	 壓電材料常數表  ……………………………………………158
圖4.1	 應力在第一象限波前圖  ……………………………………159
圖4.2	 應力在第二象限波前圖  ……………………………………160
圖4.3.1	 情況一： ， 應力暫態圖  …………………161
圖4.3.2	 情況二： ， 應力暫態圖  …………………162
圖4.3.3	 情況三： ， 應力暫態圖  …………………163
圖4.3.4	 情況四： ， 應力暫態圖  …………………164
圖4.3.5	 情況五： ， 應力暫態圖  …………………165
圖4.3.6	 情況六： ， 應力暫態圖  …………………166
圖4.4.1	 情況一： ， 應力暫態圖  …………………167
圖4.4.2	 情況二： ， 應力暫態圖  ………………168
圖4.4.3	 情況三： ， 應力暫態圖  ………………169
圖4.4.4	 情況四： ， 應力暫態圖  ………………170
圖4.4.5	 情況五： ， 應力暫態圖  ………………171
圖4.4.6	 情況六： ， 應力暫態圖  ………………172
圖4.5	 含靜止裂紋之壓電材料之應力強度因子  …………………173
圖4.6	 含靜止裂紋之壓電材料之電位移強度因子  ………………174

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