Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-18T22:49:30.506Z Has data issue: false hasContentIssue false
  • English
  • Français

A Cylindrically Anisotropic Tube Containing a Mixed Dislocation

Published online by Cambridge University Press:  05 May 2011

C.-H. Wang
C.-H. Wang*
Affiliation:
Department of Aeronautical Engineering, National Formosa University, Yunlin County, Taiwan 63201, R.O.C.
*
*Associate Professor
Get access

Abstract

This 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.

Keywords

Cylindrically anisotropicTubeDislocationState space.
Type
Articles
Information
Journal of Mechanics , Volume 26 , Issue 1 , March 2010 , pp. 71 - 80
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Lekhnitskii, S. G.Theory of Elasticity of an Anisotropic Body (translated from the revised Russian edition, 1977), Mir Publishing, Moscow (1981).Google Scholar
2.Pagano, N. J., “The Stress Field in a Cylindrically Anisotropic Body Under Two-Dimensional Surface Traction,” Journal of Applied Mechanics, ASME, 39, pp. 791–796 (1972).CrossRefGoogle Scholar
3.Chen, T., Chung, C. T. and Lin, W. L., “A Revisit of a Cylindrically Anisotropic Tube Subjected to Pressuring, Shearing, Torsion, Extension and a Uniform Temperature Change,” International Journal of Solids and Structures, 37, pp. 5143–5159 (2000).CrossRefGoogle Scholar
4.Kollar, L. P. and Springer, G. S., “Stress Analysis of Anisotropic Laminated Cylinders and Cylindrical Segments,” International Journal of Solids and Structures, 29, pp. 1499–1517 (1992).CrossRefGoogle Scholar
5.Jolicoeur, C. and Cardou, O. O.“Analytic Solution for Bending of Coaxial Orthotropic Cylinders,” Journal of Engineering Mechanics, ASCE, 120, pp. 2556–2574(1994).CrossRefGoogle Scholar
6.Ting, T. C. T.“Pressuring, Shearing, Torsion and Extension of a Circular Tube or Bar of a Cylindrically Anisotropic Material,” Proceedings of the Royal Society A, Mathematical, Physcal and Engineering Sciences, 452, pp. 2397–2421 (1996).Google Scholar
7.Ting, T. C. T.“New Solutions to Pressuring, Shearing, Torsion and Extension of a Circular Tube or Bar,” Proceedings of the Royal Society A, Mathematical, Physcal and Engineering Sciences, 455, pp. 3527–3542 (1999).CrossRefGoogle Scholar
8.Bahar, L. Y., “A State Space Approach to Elasticity,” Journal of the Franklin Institute, 229, pp. 33–41 (1975).CrossRefGoogle Scholar
9.Tarn, J. Q.“A State Space Formalism for Anisotropic Elasticity, Part II: Cylindrical Anisotropy,” International Journal of Solids and Structures, 39, pp. 5157–5172(2002).CrossRefGoogle Scholar
10.Tarn, J. Q. and Wang, Y. M.“Laminated Composite Tubes Under Extension, Torsion, Bending, Shearing and Pressuring: A State Space Approach,” International Journal of Solids and Structures, 38, pp. 9053–9075 (2001).CrossRefGoogle Scholar
11.Mura, T.Micromechanics of Defect in Solids, 2nd Edition, Martinus Nijhoff, Dordrecht (1987).CrossRefGoogle Scholar
12.Alshits, V. I. and Kirchner, H. O. K.“Cylindrically Anisotropic, Radially Inhomogeneous Elastic Materials,” Proceedings of the Royal Society A, Mathematical, Physcal and Engineering Sciences, 457, pp. 671–693 (2001).CrossRefGoogle Scholar
13.Weertman, J. and Weertman, J. R.Elementary Dislocation Theory, Oxford University Press, New York (1992).Google Scholar
14.Ting, T. C. T.Anisotropic Elasticity-Theory and Applications, Oxford University Press, New York (1996).CrossRefGoogle Scholar
15.Pease, M. C., Methods of Matrix Algebra, Academic Press, New York (1965).Google Scholar
16.Dundurs, J. “On the Interaction of a Screw Dislocation with Inhomogeneities,” Recent Advances in Engineering Science, 2nd Ed., A.C. Eringen, Gordon and Breach, pp. 223–233 (1967).Google Scholar
17.Dundurs, J. and Mura, T.“Interaction Between an Edge Dislocation and a Circular Inclusion,” Journal of Mechanics and Physics of Solids, 12, pp. 177–189 (1964).CrossRefGoogle Scholar