APPLICATION OF THE CONFORMAL MAPPING AND THE COMPLEX PATH-INDEPENDENT INTEGRALS TO THE LOCATION OF ELLIPTIC HOLES AND INCLUSIONS IN PLANE ELASTICITY PROBLEMS

The classical method of conformal mapping, which was successfully used for the solution of problems of elliptical holes and inclusions (either rigid or elastic), is combined with the more recent method of complex path-independent integrals for the location of an elliptical hole or inclusion inside an infinite plane isotropic elastic medium by using information about one or more complex potentials of plane isotropic elasticity along a closed contour surrounding the elliptical hole or inclusion. The method constitutes one more generalization of the relevant elementary methods for the location of poles of meromorphic functions in the complex plane and is simply based on the Cauchy residue theorem of complex analysis. The complex path-independent integrals used here are evaluated in the physical plane of the specimen. A numerical application of the method is made, extensive numerical results are presented and future generalizations of the method are reported in brief. © 1990.