Properties of integral operators and solutions for complex variable boundary integral equation in plane elasticity for multiply connected regions

This paper studies properties of integral operators and solutions for CVBIE (complex variable boundary integral equation) in plane elasticity for multiply connected regions. Four cases for considered regions are studied. For the individual case, we study (a) the domain field equality, (b) the null field BIE and (c) the usual CVBIE. Properties of integral operators or the kernels are studied in detail, which is based on the properties of Cauchy type integral. The Neumann problem is considered. It is shown that for finite region cases (2 and 3) the CVBIE allow three modes of rigid motion along contours under the traction free condition. In addition, for infinite region cases (4 and 5) the CVBIE does not allow three modes of rigid motion.