Numerical solution of the t-version complex variable boundary integral equation for the interior region in plane elasticity

This paper suggests the t-version complex variable boundary integral equation (CVBIE) for the interior region in plane elasticity. All the kernels in the t-version CVBIE are expressed explicitly. The property for the operator acting upon the displacement is studied. It is proved that there are three types of rigid mode movement of displacement for the t-version CVBIE, if the boundary is assumed under a traction free condition. Discretization of the t-version CVBIE is suggested. For the hypersingular integral, the integration is carried out exactly in the concept of Hadamard׳s finite part integral. Two particular examples which have known solution beforehand are used to examine the accuracy in computation. The Neumann and the Dirichlet boundary value problems are examined numerically. It is proved that the computation error is acceptable in the examples.