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Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

Published online by Cambridge University Press:  05 May 2011

C. K. Chao  and
B. Gao
C. K. Chao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R. O. C.
B. Gao*
Affiliation:
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R. O. C.
*
*Professor
**Graduate student
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Abstract

The problem of two circular inclusions of arbitrary radii and of different elastic moduli, which are perfectly bonded to an infinite matrix subjected to arbitrary loading, is solved by the heterogenization technique. This implies that the solution of the heterogeneous problem can be readily obtained from that of the corresponding homogeneous problem by a simple algebraic substitution. Based on the method of successive approximations and the technique of analytical continuation, the solution is formulated in a manner which leads to an approximate, but arbitrary accuracy, result. The present derived solution can be also applied to the problem with straight boundaries. Both the problem of two circular inclusions embedded in an infinite matrix and the problem of a circular inclusion embedded in a half-plane matrix are considered as our examples to demonstrate the use of the present approach.

Keywords

Analytical continuationHeterogenization.
Type
Articles
Information
Journal of Mechanics , Volume 14 , Issue 2 , June 1998 , pp. 67 - 73
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1998

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References

REFERENCES

1.Zimmerman, R. B., “Stress Singularity Around Two Nearby Holes,” Mechanics Research Communications, Vol. 15, pp. 87–90 (1988).CrossRefGoogle Scholar
2.Ling, C. B., “On the Stresses in a Plate Containing Two Circular Holes,” J Appl Phys., Vol. 19, pp. 77–82(1948).CrossRefGoogle Scholar
3.Duan, Z. P., Kienzler, R., and Herrmann, G., “An Integral Equation Method and Its Application to Defect Mechanics,” J. Meek Phys. Solids, Vol. 36, pp. 539–562 (1986).CrossRefGoogle Scholar
4.Callias, C. B. and Markenscoff, X., “Singular Asymptotics Analysis for the Singularity at a Hole near a Boundary,” Quarterly of Applied Mathematics, Vol. 47, pp. 233–245 (1989).CrossRefGoogle Scholar
5.Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, Holland (1953).Google Scholar
6.Gong, S. X. and Meguid, S. A., “Interacting Circular Inclusions in Plane Elastostatics,” Ada Mechanica, Vol. 99, pp. 49–60 (1993).CrossRefGoogle Scholar
7.Chao, C. K., Shen, M. H. and Fung, C. K., “On Multiple Circular Inclusions in Plane Thermoelasticity”, Int. J. Solids and Structures, Vol. 34, pp. 1873–1892(1997).CrossRefGoogle Scholar
8.Chao, C. K. and Young, C. W., “Antiplane Interaction of a Crack with a Circular Inclusion in an Elastic Half-Plane,” J. Eng. Mechs., ASCE, Vol. 124, pp. 167–175(1998).Google Scholar
9.Sokolnikoff, I. S., Mathematical Theory of Elasticity, Krieger Publishing Company, Fla (1983).Google Scholar
10.Chao, C. K. and Lee, J. Y., “Interaction between a Crack and a Circular Elastic Inclusion under Remote Uniform Heat Flow,” Int. J. Solids and Structures, Vol. 33, pp. 3865–3880 (1996).CrossRefGoogle Scholar
11.Honein, E., Honein, T. and Herrmann, G., “Further Aspects of the Elastic Field for Two Circular Inclusions in Antiplane Elastostatics,” J. Appl. Mech., ASME, Vol. 59, pp. 774–779 (1992).CrossRefGoogle Scholar
12.Haddon, R. A. W., “Stresses in an Infinite Plate with Two Unequal Circular Holes,” Quart. J. Mech. and Appl. Math., Vol. XX, pp. 277–291 (1967).CrossRefGoogle Scholar