Antiplane deformations for anisotropic multilayered media by using the coordinate transform method

Green's functions for anisotropic elastic multilayered media subjected to a ntiplane shear deformation are presented in this study. The antiplane shear deformation due to a concentrated shear force and screw dislocation in an arbitrary layer was investigated in detail. A linear coordinate transformat ion is introduced in this study to simplify the problem. The linear coordin ate transformation reduces the anisotropic multilayered problem to an equiv alent isotropic problem without complicating the geometry of the problem. E xplicit analytical solutions were derived using the Fourier transform and t he series expansion technique. The complete solutions for the multilayered problem consist only of the simplest solutions obtained from an infinite ho mogeneous medium with concentrated loadings. Numerical results for the full -field stress distribution in multilayered media subjected to a point body force are presented. These numerical results were compared with the solutio ns obtained by considering the multilayered medium as one layer with effect ive elastic constants determined from the averaged material constants of th e multilayered medium. It is found that the shear stress tau (yz) of the ho mogeneous one layer solution is a very good approximation of the result for the multilayered medium; however, the shear stress tau (xz) in these two s olutions has a large discrepancy due to the fact that tau (xz) is discontin uous at the interfaces of the multilayered medium.