The complex one-sided integrals of cauchy and hadamard and application to boundary element method

The definitions of complex integrals of Cauchy and Hadamard with the singular point coinciding with the end point of the integration curve are proposed. It is shown that the new integrals satisfy most of the properties of the regular ones, including the change of variables. It is also shown that the Cauchy principal value (CPV) and Hadamard finite-part (HFP) integrals can be considered as a sum of the new type integrals. The application to numerical solution by the boundary element method (BEM) and the complex hypersingular integral equation (CHSIE) for the multiregions of interacting elastic bodies and bodies with cracks and holes is discussed. The different ways to place the collocation points are considered. The numerical results for the problems of circular hole and circular elastic inclusion in infinite plate indicated that the appropriate choice of the approximating functions leads to a high accuracy of the calculation. Applications of the new technique to geomechanics problems are discussed.