 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 39, Issue 1 / 2004 | Next article >> |
| R. V. Goldstein and E. I. Shifrin, "Integral equations of the problem of an elastic inclusion. Complete analytical solution of the problem of an elliptic inclusion," Mech. Solids. 39 (1), 36-55 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
36-55 |
| Title |
Integral equations of the problem of an elastic inclusion. Complete analytical solution of the problem of an elliptic inclusion |
| Author(s) |
R. V. Goldstein (Moscow)
E. I. Shifrin (Moscow) |
| Abstract |
We consider the problem of an isotropic elastic space containing an isotropic
elastic inclusion. Using a generalization of the Eshelby method, we construct
new integral equations for the stress tensor components inside the inclusion.
Detailed investigation is carried out in the case of the plane problem and an
elliptic inclusion. In this case, explicit analytical expressions are obtained
for the stress tensor components inside and outside the inclusion. Using the
procedure of passing to the limit, we construct solutions for an elliptic hole
and a rigid elliptic inclusion. In the case of circular inclusions,
simplified formulas for stresses are obtained as a special case of the general
formulas. For all special cases found in the literature in which
analytical expressions of the stresses have been constructed, the solutions
obtained in this paper are compared with those obtained previously. |
| References |
| 1. | V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze,
Three-Dimensional Mathematical Problems in Elasticity and Thermoelasticity [in Russian],
Nauka, Moscow, 1976. |
| 2. | V. Z. Parton and P. I. Perlin,
Integral Equations of Elasticity [in Russian], Nauka, Moscow, 1977. |
| 3. | N. J. Hardiman, " Elliptic elastic inclusion in an infinite
elastic plane," Quart. J. Mech. Appl. Math., Vol. 7, pp. 226-230, 1954. |
| 4. | J. Eshelby,
"Determination of the elastic stress field caused by an ellipsoidal
inclusion and related problems," in Continuous Dislocation Theory [Russian translation],
pp. 103-139, Izd-vo Inostr. Lit-ry., Moscow, 1963. |
| 5. | R. V. Goldstein and E. I. Shifrin,
Plane Problem for the Stress State Caused by Phase Transitions in an
Elliptic Region. Preprint No. 714 [in Russian], Institute for Problem in
Mechanics, Russian Academy of Sciences, Moscow, 2003. |
| 6. | N. I. Muskhelishvili, Some Basic Problems in Mathematical Elasticity [in Russian],
Nauka, Moscow, 1966. |
| 7. | L. I. Sedov, Continuum Mechanics [in Russian], Nauka, Moscow, 1976. |
| 8. | S. P. Timoshenko and J. Goodier, Theory of Elasticity [Russian translation], Nauka,
Moscow, 1979. |
| 9. | H. Hahn,, Theory of Elasticity [Russian translation], Mir, Moscow, 1988. |
| 10. | P. F. Papkovich, Theory of Elasticity, Gos. Izd-vo Oboron. Prom., Moscow, Leningrad,
1939. |
| 11. | J. N. Goodier, "Concentration of stress around spherical and
cylindrical inclusions and flaws," J. Appl. Mech., APM-55-7, pp. 39-44,
1933. |
|
| Received |
08 October 2003 |
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