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Near-Tip Field and the Associated Path-Independent Integrals for Anisotropic Composite Wedges

Published online by Cambridge University Press:  05 May 2011

Kuang-Chong Wu
Kuang-Chong Wu*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Professor
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Abstract

The asymptotic fields in an elastic anisotropic composite wedge are considered for a wide range of boundary conditions. It is shown that the eigenfunctions for the near-field and far-field are dual as they are generated by the same set of eigenvalues in general. If the boundary conditions on the wedge faces are the same, an additional eigenfunction may appear in the far-field. Moreover the dual eigenfunctions are used to derive path-independent integrals that relate the near-field to the far-field.

Keywords

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Type
Articles
Information
Journal of Mechanics , Volume 17 , Issue 1 , March 2001 , pp. 21 - 28
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2001

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References

REFERENCES

1Williams, M. L., “Stress Singularities Resulting from Various Conditions in an Angular Corners of Plates in Extension,” ASME Journal of Applied Mechanics, 19, pp. 526–528 (1952).CrossRefGoogle Scholar
2Dempsey, J. P. and Sinclair, G. B., “On the Stress Singularities in the Plane Elasticity of the Composite Wedge,” Journal of Elasticity, 9, pp. 373–391 (1979).CrossRefGoogle Scholar
3Sih, G. C., Paris, P. C. and Irwin, G. R., “On Cracks in Rectilinearly Anisotropic Bodies,” International Journal of Fracture Mechanics, 1, pp. 189–302 (1965).CrossRefGoogle Scholar
4Bogy, D. B., “The Plane Solution for Anisotropic Elastic Wedges under Normal and Shear Loading,” ASME Journal of Applied Mechanics, 39, pp. 1103–1109 (1972).CrossRefGoogle Scholar
5Kuo, M. C. and Bogy, D. B., “Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges,” ASME Journal of Applied Mechanics, 41, pp. 197–203 (1974).CrossRefGoogle Scholar
6Stroh, A. N., “Steady State Problems in Anisotropic Elasticity,” Journal of Mathematical Physics, 41, pp. 77–103 (1962).CrossRefGoogle Scholar
7Ting, T. C. T. and Chou, S., “Edge Singularities in Anisotropic Composites,” International Journal of Solids and Structures, 17, pp. 1057–1068 (1981).CrossRefGoogle Scholar
8Wu, K.-C. and Chang, F.-T., “Near-Tip Fields in a Notched Body with Dislocations and Body Forces,” ASME Journal of Applied Mechanics, 60, pp. 936–941 (1993).CrossRefGoogle Scholar
9Mantic, V., Paris, F. and Canas, J., “Stress Singularities in 2D Orthotropic Corners,” International Journal of Fracture, 83, pp. 67–90 (1997).CrossRefGoogle Scholar
10Belov, A. Y. and Kirchner, H. O. K., “Universal Weight Functions for Elastically Angularly Inhomogeneous Media with Notches and Cracks,” Philosophical Magazine, A73, pp. 1621–1646 (1996).CrossRefGoogle Scholar
11Kirchner, H. O. K., “Elastically Anisotropic Angularly Inhomogeneous Media I. a New Formalism,” Philosophical Magazine, B60, pp. 423–432 (1989).CrossRefGoogle Scholar
12Bueckner, H. F., “A Novel Principle for the Computation of Stress Intensity Factors,” Zeitschrift Fur Angewandte Mathematik und Mechanik, 50, pp. 529–546 (1970).Google Scholar
13Sham, T. L. and Bueckner, H. F., “The Weight Function Theory for Piecewise Homogeneous Isotropic Notches in Antiplane Strain,” ASME Journal of Applied Mechanics, 55, pp. 596–603 (1988).CrossRefGoogle Scholar
14Barnett, D. M. and Lothe, J., “Line Force Loadings on Anisotropic Half-Spaces and Wedges,” Physica Norvegica, 8, pp. 13–22 (1975).Google Scholar
15Ting, T. C. T., “Line Forces and Dislocations in Anisotropic Elastic Composite Wedges and Spaces,” Physica Status Solidi B, 146, pp. 81–90 (1988).CrossRefGoogle Scholar
16Carothers, S. D., “Plane Strain in a Wedge,” Proceedings of the Royal Society of Edingburgh, 23, pp. 292–306 (1912).Google Scholar
17Sternberg, E. and Koiter, W., “The Wedge under a Concentrated Couple: a Paradox in the Two-Dimensional Theory of Elasticity,” ASME Journal of Applied Mechanics, 25, pp. 575–581 (1958).CrossRefGoogle Scholar
18Hwu, C. and Ting, T. C. T., “Solutions for the Anisotropic Wedges at Critical Angles,” Journal of Elasticity, 24, pp. 1–20 (1990).CrossRefGoogle Scholar
19Belov, A. Y. and Kirchner, H. O. K., “Critical Angles in Bending of Rotationally Inhomogeneous Elastic Wedges,” ASME Journal of Applied Mechanics, Vol. 62, pp. 429–440 (1995).CrossRefGoogle Scholar
20Ting, T. C. T., Anisotropic Elasticity — Theory and Application, Oxford University Press, New York (1996).CrossRefGoogle Scholar
21Kirchner, H. O. K., “Weight Functions for Notches: Constructive and Variational Definition,” ASME Journal of Applied Mechanics, Vol. 64, pp. 270–274 (1997).CrossRefGoogle Scholar