The Theoretical Analysis of Anisotropic Multi-layered Medium and Punch Problem

• Main Authors: Ru-Li Lin, 林儒禮
• Other Authors: Chien-Ching Ma
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/30057061835923527670

博士 === 國立臺灣大學 === 機械工程學研究所 === 87 === The method of image is a technique that uses superposition of known solution to solve another problems. The method had been used powerfully to deal two-dimensional elastic anisotropic bimaterials problem and the nature of image singularities were also discussed in detail. But for isotropic material, the degenerate case of anisotropic case, the image singularities are not simply forces and dislocations any more. The aim of this paper is to investigate the Green’s function of the half plane with straight boundary, and to discuss in detail the structure of image singularities on the image point. It is hard to obtain the analytical solution for the anti plane problems of anisotropic multi-layered medium due to the material constants and boundary condition. With aid of the technique of Fourier transform and series expansion, the solutions can be derived in the study. The physical meanings of the solution can be regarded as the application of image method. The same method also used to obtain the solutions for the plane problem of anisotropic multi-layered medium. By constructing the relation of surface displacement and traction for anisotropic half plane, it can transfer the punch problem, the mixed boundary value problem, into the boundary value problem. Combining the surface traction of half plane and the Green’s functions for anisotropic planar and axisymmetric problems, it can obtain the first order approximation for the punch problem of thin layer.