Transfer matrix method for the solution of multiple elliptic layers with different elastic properties. Part II: exterior finite elliptic matrix case

Abstract

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. In the present study, the exterior layer is a finite confocal elliptic layer. Some derivations in the present study are similar to those in Chen (Acta Mech 2014). However, some derivations in the present study are quite different from those in Chen (Acta Mech 2014). Equations for evaluating the coefficients in the Laurent series for complex potentials are suggested, which are derived from the transfer matrix and the boundary condition. A numerical example for the case of an elliptic inclusion and two confocal elliptic layers is provided in this paper.