Potential fields caused by point sources in regions with apertures and foreign inclusions

A semi-analytic approach is developed for obtaining potential fields generated by point sources in regions embedded with foreign inclusions and containing holes of various shape. This study promotes an extension of the range of effective implementation of the Green's function version of the boundary integral equation method in mechanics of contemporary materials. Equivalents of Green's functions are obtained to boundary-contact value problems posed for Laplace equation on piecewise homogeneous multiply connected regions. Dirichlet, Neumann and Robin boundary conditions can be imposed on the outer boundary of the region and on contours of the apertures, while the ideal contact conditions are assumed on the interfacial contours. Source points could be located either outside or inside the inclusion. A Green's function modification of the method of functional equations is applied. A number of illustrative examples included to show the potential of the approach.