 | | 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 |
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| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| Ya.M. Pasternak and G.T. Sulim, "Plane Problem of Elasticity for an Anisotropic Body with Doubly Periodic Systems of Thin Inhomogeneities," Mech. Solids. 49 (2), 162-174 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
2 |
Pages |
162-174 |
| DOI |
10.3103/S002565441402006X |
| Title |
Plane Problem of Elasticity for an Anisotropic Body with Doubly Periodic Systems of Thin Inhomogeneities |
| Author(s) |
Ya.M. Pasternak (Lutsk National Technical University, Lvivska 75, Lutsk, 43018 Ukraine, pasternak@ukrpost.ua)
G.T. Sulim (Ivan Franko National University of Lviv, Universytetskaya 1, Lviv, 79000 Ukraine, sulym@franko.lviv.ua) |
| Abstract |
A system of integral equations of the boundary element method for studying doubly periodic systems of thin inclusions in anisotropic bodies is constructed. Several dependences for determining the mean stresses and strains of a composite with regular systems of thin inhomogeneities are obtained. Numerical procedures of the proposed method are implemented, and generalized stress intensity factors are calculated together with the effective elasticity moduli of a composite with doubly periodic systems of thin elastic inclusions. |
| Keywords |
boundary element method, generalized stress intensity factors, thin inclusion, crack, anisotropy, effective characteristics of a composite |
| References |
| 1. | Yu. F. Kovalenko and R. L. Salganik,
"Fractured Inhomogeneities and Their Influence on Effective Mechanical Characteristics,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 5, 76-86 (1977)
[Mech. Solids (Engl. Transl.)]. |
| 2. | J. Wang, F. Fang, and B. L. Karihaloo,
"Asymptotic of Multiple Crack Interaction and Prediction of Effective Modulus,"
Int. J. Solids Struct.
37 (31), 4261-4273 (2000). |
| 3. | G. S. Wang,
"The Interaction of Doubly Periodic Cracks,"
Theor. Appl. Fract. Mech.
42 (3), 249-294 (2004). |
| 4. | C. Y. Dong and K. Y. Lee,
"Numerical Analysis of Doubly Periodic Array of Cracks/Rigid-Line Inclusions
in an Infinite Isotropic Medium Using the Boundary Integral Equation Method,"
Int. J. Fract.
133 (4), 389-405 (2005). |
| 5. | M. P. Savruk,
Two-Dimensional Problems of Elasticity for Bodies with Cracks
(Naukova Dumka, Kiev, 1981)
[in Russian]. |
| 6. | A. M. Lin'kov,
Complex Method of Boundary Integral Equations in Elasticity
(Nauka, St. Petersburg, 1999)
[in Russian]. |
| 7. | G. T. Sulim,
Foundations of Mathematical Theory of Thermoelastic Equilibrium of Deformed Solids with Thin Inclusions
(Doslidno-Vidavnich. Tsentr NTSh, Lviv, 2007)
[in Ukrainian] |
| 8. | L. A. Fil'shtinskii,
"Double Periodic Elasticity Problem for Anisotropic Medium with Curvilinear Cuts,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 116-124 (1977)
[Mech. Solids (Engl. Transl.)]. |
| 9. | H. J. Choi,
"A Periodic Array of Cracks in a Functionally Graded Nonhomogeneous Medium Loaded
under in-Plane Normal and Shear,"
Int. J. Fract.
88 (2), 107-128 (1997). |
| 10. | V. V. Bozhidanik and O. V. Maksimovich,
Elastic and Limit Equilibrium of Anisotropic Plates with Holes and Cracks
(LDTU, Lutsk, 2003)
[in Ukrainian] |
| 11. | J. Xiao and C. Jiang,
"Exact Solution for Orthotropic Materials Weakened by Doubly Periodic Cracks
of Unequal Size under Antiplane Shear,"
Acta Mechanica Solida Sinica
22 (1), 53-63 (2009). |
| 12. | P. Malits,
"Doubly Periodic Array of Thin Rigid Inclusions in an Elastic Solid,"
Quar. J. Mech. Appl. Math.
63 (2), 115-144 (2010). |
| 13. | L. T. Berezhnitskii, V. V. Panasyuk, and N. G. Stazhchuk,
Interaction of Rigid Linear Inclusions and Cracks in Deformable Body
(Naukova Dumka, Kiev, 1983)
[in Russian]. |
| 14. | V. Opanasovich, V. Porochovsky, and M. Delyavsky,
"Antiplane Deformation of Isotropic Body with a Periodic System of Thin Rectilinear Inclusions,"
J. Theor. Appl. Mech.
37 (1), 65-79 (1999). |
| 15. | A. S. Kosmodamianskii,
Stress State of Anisotropic Media with Holes and Cavities
(Vishcha Shkola, Kiev, 1976)
[in Russian]. |
| 16. | V. N. Dolgikh and L. A. Fil'shtinskii,
"Model of an Anisotropic Medium Reinforced by Thin Tapes,"
Prikl. Mekh.
15 (4), 24-30 (1979)
[Int. Appl. Mech. (Engl. Transl.)
15 (4), 292-296 (1979)]. |
| 17. | D. Clouteau, M. I. Elhabre, and D. Aubry,
"Periodic BEM and FEM-BEM Coupling,"
Comp. Mech.
25 (6), 567-577 (2000). |
| 18. | Ia. M. Pasternak,
"Coupled 2D Electric and Mechanical Fields in Piezoelectric Solids Containing Cracks
and Thin Inhomogeneities,"
Engng Anal. Bound. Elem.
35 (4), 678-690 (2011). |
| 19. | Ia. M. Pasternak and N. T. Sulym,
"Thin Inclusions Theory Integral Equations Numerical Solutions
Using the Boundary Element Method Procedure,"
in Proc. Int. Conf. "Integral Equations - 2010"
(PAIS, Lviv, 2010),
pp. 104-108. |
| 20. | Ya. S. Podstrigach,
"Conditions of Stress and Displacement Jump on a Thin-Wall Elastic Inclusion in Continuum,"
Dokl. Ukr. Akad. Nauk. Ser. A,
No. 12, 30-32 (1982). |
| 21. | G. P. Cherepanov,
"Method of External and Internal Expansions in Elasticity,"
in Mechanics of Deformable Bodies and Structures
(Mashinostroenie, Moscow, 1975),
pp. 502-507
[in Russian]. |
| 22. | T. C. T. Ting,
Anisotropic Elasticity: Theory and Applications
(Oxford Univ. Press, N.Y., 1996). |
| 23. | S. G. Lekhnitskii,
Theory of Elasticity of Anisotropic Body
(Nauka, Moscow, 1977)
[in Russian]. |
| 24. | Ia. M. Pasternak and G. T. Sulym,
"Dual Boundary Element Method for Problems of the Theory of Thin Inclusions,"
Mat. Met. Fiz.-Mekh. Polya
53 (2), 46-57 (2010)
[J. Math. Sci. (Engl. Transl.)
178 (4), 421-434 (2011)]. |
| 25. | F. W. Olver et al. (Editors),
NIST Handbook of Mathematical Functions
(Cambridge Univ. Press, N.Y. 2010). |
| 26. | A. Portella, M. N. Aliabadi, and D. P. Rooke,
"The Dual Boundary Element Method: Effective Implementation for Crack Problems,"
Int. J. Numer. Engng
33 (6), 1269-1287 (1992). |
| 27. | J. H. Xiao, Y. L. Xu, and C. P. Jiang,
"Exact Solutions to the Antiplane Problem of Doubly Periodic Conducting Rigid Line Inclusions
of Unequal Size in Piezoelectric Materials,"
ZAMM
91 (5), 413-424 (2011). |
| 28. | E. Pan,
"A General Boundary Element Analysis of 2D Linear Elastic Fracture Mechanics,"
Int. J. Fract.
88 (1), 41-59 (1997). |
|
| Received |
06 September 2011 |
| Link to Fulltext |
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