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Notation

Before we apply FM-BIEM to crack problems we summarise the notations about a crack. In this thesis we denote a crack by $S(\in R^3)$ and assume that S is a union of smooth non-self-intersecting curved surfaces having edges $\partial S$ and a unit normal vector $\mbox{\boldmath$\space n $ }$ (See Fig.3.1).
  
Figure 3.1: Notations about a crack
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Also, we denote $S+\partial S$ by $\overline{S}$ and the superscript + (-) indicates the limit on S from the positive (negative) side of S where the positive side indicates the one into which the unit normal $\mbox{\boldmath$\space n $ }$ points. In this thesis we denote the discontinuity of u across S by $\phi(:=u^+ - u^-)$ and call $\phi$ the crack opening displacement though $\phi$ may not necessarily be a physical displacement. In crack problems we impose the regularity condition $\phi=0 ~\mbox{on}~ \partial S$. This condition guarantees the uniqueness of the solution. The above notations are used throughout this thesis unless stated otherwise.



Ken-ichi Yoshida
2001-07-28