Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T14:16:35.219Z Has data issue: false hasContentIssue false
  • English
  • Français

On Approximate Solutions for Two-Dimensional Thermoelastic Problems with a Nearly Circular Hole

Published online by Cambridge University Press:  05 May 2011

Chung-Hao Wang  and
Ching-Kong Chao
Chung-Hao Wang*
Affiliation:
Department of Aeronautical Engineering, National Huwei Institute of Technology, Huwei, Yunlin, Taiwan 632, R.O.C.
Ching-Kong Chao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 106, R.O.C.
*
*Associate Professor
**Professor
Get access

Abstract

The general approximate solutions for the two-dimensional thermoelastic problems with a nearly circular hole are provided in this study. Based on Stroh formalism and the method of conformal mapping, the boundary perturbation analysis is applied to solve the problems of a hole with arbitrary shape. The radius of the hole considered here is represented as a sum of a reference constant and a perturbation magnitude that is expanded into a Fourier series. In order to illustrate the applicability and efficiency of the present approach, special examples associated with polygonal hole problems are solved explicitly and discussed in detail. Since the general solutions have not been found in the literature, comparison is made with some special cases for which the analytical solutions exist, which shows that our proposed method is effective and general.

Keywords

ThermoelasticityAnisotropicNearly-circular holeelliptical hole
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 149 - 160
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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

REFERENCES

1Florence, A. L. and Goodier, J. N., “Thermal Stress at Spherical Cavities and Circular Holes in Uniform Heat Flow,” J. Appl. Mech., 26, pp. 293–294 (1959).CrossRefGoogle Scholar
2Florence, A. L. and Goodier, J. N., “Thermal Stress due to Disturbance of Uniform Heat Flow by an Insulated Ovaloid Hole,” J. Appl. Mech., 27, pp. 635–639 (1960).CrossRefGoogle Scholar
3Muskhelishvili, N. I., Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff, Groningen (1953).Google Scholar
4Chen, W. T., “Plane Thermal Stress at an Insulated Hole Under Uniform Heat Flow in an Orthotropic Medium,” J. Appl. Mech., 34, pp. 133–136 (1967).CrossRefGoogle Scholar
5Green, A. E. and Zerna, W., Theoretical Elasticity, Oxford University Press, London, England (1954).Google Scholar
6Stroh, A. N., “Dislocations and Cracks in Anisotropic Elasticity,” Phil. Mag., 7, pp. 625–646 (1958).CrossRefGoogle Scholar
7Stroh, A. N., “Steady State Problems in Anisotropic Elasticit.”, J. Math. Phys., 41, pp. 77–103 (1962).CrossRefGoogle Scholar
8Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, MIR, Moscow (1981).Google Scholar
9Hwu, C. and Ting, T. C. T., “Two-Dimensional Problems of the Anisotropic Elastic Solid with an Elliptic Inclusion,” Q. J. Mech. Appl. Math., 42(4), pp. 553–572 (1989).CrossRefGoogle Scholar
10Hwu, C., “Thermal Stresses in an Anisotropic Plate Disturbed by an Insulated Elliptic Hole or Crack,” J Appl. Mech., 57, pp. 916–922 (1990).CrossRefGoogle Scholar
11Tarn, J. Q. and Wang, Y. M., “Thermal Stresses in Anisotropic Bodies with a Hole or a Rigid Inclusion,” J. Thermal Stresses, 16, pp. 455–471 (1993).CrossRefGoogle Scholar
12Chao, C. K. and Shen, M. H., “Thermal Stresses in a Generally Anisotropic Body with an Elliptic Inclusion Subject to Uniform Heat Flow,” J Appl. Mech., 65, pp. 51–58 (1998).CrossRefGoogle Scholar
13Gao, H., “Stress Analysis of Holes in Anisotropic Elastic Solids: Conformal Mapping and Boundary Perturbation,” Q. J. Mech. Appl. Math., 45(2), pp. 149–168 (1992).CrossRefGoogle Scholar
14Ting, T. C. T., Anisotropic Elasticity — Theory and Applications, Oxford Science Publications, New York (1996).CrossRefGoogle Scholar
15Barnett, D. M. and Lothe, J., “Synthesis of the Sextic and the Integral Formalism for Dislocation, Green's Function and Surface Waves in Anisotropic Elastic Solids,” Phys. Norv., 7, pp. 13–19 (1973).Google Scholar
16Ingebrigsten, K. A. and Tonning, A., “Elastic Surface Waves in Crystals,” Phys. Rev., 184, pp. 942–951 (1969).CrossRefGoogle Scholar
17Ting, T. C. T. and Hwu, C., “Sextic Formalism in Anisotropic Elasticity for Almost Non-semisimple Matrix N,” Int. J. Solids Struct., 24(1), pp. 65–76 (1988).CrossRefGoogle Scholar
18Hwu, C., “Correspondence Relations Between Anisotropic and Isotropic Elasticity,” The Chinese J. Mech., 12(4), pp. 483–493 (1996).Google Scholar
19Kattis, M. A., “Thermoelastic Plane Problems with Curvilinear Boundaries,” Acta Mechanica, 87, pp. 93–103 (1991).CrossRefGoogle Scholar
20Yan, G. and Ting, T. C. T., “The r–1/2 (1n r) singularities at Interface Cracks in Monoclinic and Isotropic Bimaterials due to Heat Flow,” J. Appl. Mech., 60, pp. 432–437 (1993).CrossRefGoogle Scholar