A Cylindrically Anisotropic Tube Containing a Mixed Dislocation

Abstract

AbstractThis study presents an analytical methodology for solving an elastic problem of a cylindrically anisotropic tube infused with eigenstrains. The general solutions for the particular case of a tube containing a mixed dislocation are also provided. The mainframe of this analysis is based on the state space formulation in conjunction with the theory of eigenstrain. By using the technique of Fourier series expansion and the theory of matrix algebra on solving the state equation, the expressions of solutions are not only explicit but also compact. The dislocation considered in this study is a mixed dislocation which can be viewed as a combination of edge dislocations and a screw dislocation. In order to strengthen the feasibility of this analysis, the strategy to determine the inverse of a singular matrix is thoroughly discussed, such that the general solutions can be smoothly applied to an isotropic tube problem. The results for an isotropic tube, which are reduced from the general forms, are compared with the well-established researches of related cases in the literature. The acceptable correspondences indicate the applicability of this study. An elastic problem of a cylindrically orthotropic tube containing a dislocation is also investigated as a demonstrating example. On this example, several particular phenomenons of stress distribution on the tube surface are presented in figures and discussed.