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(a) Direct Problem

A standard argument shows that the solution to (1) is written as


where G is the fundamental solution of Laplace's equation given by

and is the crack opening displacement defined by

The unknown functions u on and on S are determined as the solutions to the following integral equations:


where the integration symbol with a superimposed = on the RHS of (4) stands for the finite part. As a matter of fact the hypersingular integral equation in (4) is obtained as one computes the normal derivative of (2) in and takes the limit onto S. A simple but rigorous proof that the limit takes the form in (4) is found for example in Nishimura & Kobayashi[31].

N. Nishimura
Thu Feb 19 01:36:51 JST 1998