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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 and assume that S is a union of smooth non-self-intersecting curved surfaces having edges and a unit normal vector (See Fig.3.1).

Also, we denote by 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 points. In this thesis we denote the discontinuity of u across S by and call the crack opening displacement though may not necessarily be a physical displacement. In crack problems we impose the regularity condition . 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