Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T14:50:53.526Z Has data issue: false hasContentIssue false
  • English
  • Français

The Inversion and Kelvin's Transformation in Plane Thermoelasticity with Circular or Straight Boundaries

Published online by Cambridge University Press:  09 October 2017

C. K. Chao ,
C. H. Wu  and
K. Ting
C. K. Chao*
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
C. H. Wu
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
K. Ting
Affiliation:
Department of Chemical and Materials EngineeringLunghwa University of Science and TechnologyTaoyuan, Taiwan
*
*Corresponding author ([email protected])
Get access

Abstract

The problem of a circular elastic inclusion perfectly bonded to a matrix of infinite extent and subjected to arbitrarily thermal loading has been solved explicitly in terms of the corresponding homogeneous problem based on the inversion and Kelvin's transformation. It is to be noted that the relations established in this paper between the stress functions are algebraic and do not involve integration or solution of some other equations. Furthermore, the transformation leading from the solution for the homogeneous problem to that for the heterogeneous one is very simple, algebraic and universal in the sense of being independent of loading considered. The case of two bonded half-planes is obtained as a limiting case.

Keywords

Plane thermoelasticityCircular inclusionBonded half-planes
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 5 , October 2018 , pp. 617 - 627
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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. Florence, L. and Goodier, J. N., “Thermal Stress at Spherical Cavities and Circular Holes in Uniform Heat Flow,” Journal of Applied Mechanics, 26, pp. 293–294 (1959).Google Scholar
2. Florence, L. and Goodier, J. N., “Thermal Stress Due to Disturbance of Uniform Heat Flow by an Insulated Ovaloid Hole,” Journal of Applied Mechanics, 27, pp. 635–639 (1960).Google Scholar
3. Chen, W. T., “Plane Thermal Stress at an Insulated Hole under Uniform Heat Flow in an Orthotropic Medium,” Journal of Applied Mechanics, 34, pp. 133–136 (1967).Google Scholar
4. Dundurs, J. and Sendeckyj, G. P., “Edge Dislocation Inside a Circular Inclusion,” Journal of Mechanics and Physics of Solids, 13, pp. 141–147 (1965).Google Scholar
5. Honein, T. and Herrmann, G., “On Bonded Inclusion with Circular or Straight Boundaries in Plane Elastostatics,” Journal of Applied Mechanics, 57, pp. 850–856 (1990).Google Scholar
6. Kattis, M. A. and Meguid, S. A., “Two-Phase Potentials for the Treatment of an Elastic Inclusion in Plane Thermoelasticity,” Journal of Applied Mechanics, 62, pp. 7–12 (1995).Google Scholar
7. Chao, C. K. and Shen, M. H., “On Bonded Circular Inclusions in Plane Thermoelasticity,” Journal of Applied Mechanics, 64, pp. 1000–1004 (1997).Google Scholar
8. Xiao, Z. M. and Chen, B. J., “On the Interaction between an Edge Dislocation and a Coated Inclusion,” International Journal of Solids and Structures, 38, pp. 2533–2548 (2001).Google Scholar
9. Muskhelishivili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen-Holland (1953).Google Scholar
10. Chao, C. K., Chen, F. M. and Lin, T. H., “The Stress Field Due to an Edge Dislocation Interacting with Two Circular Inclusions,” Journal of Mechanics, 33, pp. 161–172 (2017).Google Scholar
11. Tarn, J. Q. and Wang, Y. M., “Thermal Stresses in Anisotropic Bodies with a Hole or a Rigid inclusion,” Journal of Thermal Stresses 16, 455 (1993).Google Scholar
12. Parkus, H., Thermoelasticity, Blaisdell, Waltham, MA (1968).Google Scholar