 | | 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
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| In English (Mech. Solids): | | 3212 |
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| A.A. Belov, L.A. Igumnov, S.Yu. Litvinchuk, and V.S. Metrikin, "Application of Boundary Integral Equations for Analyzing the Dynamics of Elastic, Viscoelastic, and Poroelastic Bodies," Mech. Solids. 51 (6), 677-683 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
6 |
Pages |
677-683 |
| DOI |
10.3103/S0025654416060078 |
| Title |
Application of Boundary Integral Equations for Analyzing the Dynamics of Elastic, Viscoelastic, and Poroelastic Bodies |
| Author(s) |
A.A. Belov (Institute of Mechanics, Lobachevsky Nizhnii Novgorod State University, pr. Gagarina 23-6, GSP-1000, Nizhnii Novgorod, 603950 Russia)
L.A. Igumnov (Institute of Mechanics, Lobachevsky Nizhnii Novgorod State University, pr. Gagarina 23-6, GSP-1000, Nizhnii Novgorod, 603950 Russia)
S.Yu. Litvinchuk (Institute of Mechanics, Lobachevsky Nizhnii Novgorod State University, pr. Gagarina 23-6, GSP-1000, Nizhnii Novgorod, 603950 Russia, litvinchuk@mech.unn.ru)
V.S. Metrikin (Institute of Mechanics, Lobachevsky Nizhnii Novgorod State University, pr. Gagarina 23-6, GSP-1000, Nizhnii Novgorod, 603950 Russia) |
| Abstract |
Two approaches (classical and nonclassical) of the boundary integral equation method for solving three-dimensional dynamical boundary value problems of elasticity, viscoelasticity, and poroelasticity are considered. The boundary integral equation model is used for porous materials. The Kelvin-Voigt model and the weakly singular hereditary Abel kernel are used to describe the viscoelastic properties. Both approaches permit solving the dynamic problems exactly not only in the isotropic but also in the anisotropic case. The boundary integral equation solution scheme is constructed on the basis of the boundary element technique. The numerical results obtained by the classical and nonclassical approaches are compared. |
| Keywords |
three-dimensional problem, boundary integral equation method, anisotropy, viscoelasticity, poroelasticity |
| References |
| 1. | T. A. Cruse and F. J. Rizzo,
"A Direct Formulation and Numerical Solution
of the General Transient Elastodynamic Problem. Part I,"
J. Math. Anal. Appl.,
No. 22, 244-259 (1968). |
| 2. | T. A. Cruse and F. J. Rizzo,
"A Direct Formulation and Numerical Solution
of the General Transient Elastodynamic Problem. Part II,"
J. Math. Anal. Appl.,
No. 22, 341-355 (1968). |
| 3. | A. G. Ugodchikov and N. M. Khutoryanskii,
Boundary Element
Method in Mechanics of Deformable Solids
(Izdat. Kazan Univ., Kazan, 1986)
[in Russian]. |
| 4. | M. Schanz,
Wave Propagation in Viscoelastic and Poroelastic Continua
(Springer, Berlin, 2001). |
| 5. | F. Durbin,
"Numerical Inversion of Laplace Transforms: An Efficient Improvement
to Dubner and Abate's Method,"
Computer J.
17 (4), 371-376 (1974). |
| 6. | C. Lubich,
"Convolution Quadrature and Discretized Operational Calculus. I,"
Numer. Math.,
No. 52, 129-145 (1988). |
| 7. | C. Lubich,
"Convolution Quadrature and Discretized Operational Calculus. II,"
Numer. Math.,
No. 52, 413-442 (1988). |
| 8. | L. A. Igumnov and I. P. Markov,
"Application of the Boundary Element Method for Analyzing the Dynamics
of Anisotropic Elastic Bodies,"
Probl. Prochn. Plastichn.
76 (1), 65-69 (2014). |
| 9. | C. Y. Wang and J. D. Achenbach,
"Three-Dimensional Time-Harmonic Elastodynamic Green's Functions
for Anisotropic Solids,"
Proc. Roy. Soc. London. A
449 (1937), 441-458 (1995). |
| 10. | L. Gaul, M. Kogl, and M. Wagner,
Boundary Element Method for Engineers and Scientists
(Springer, Berlin, 2003). |
| 11. | V. A. Babeshko, "New Method for Solving Boundary Value Problems of
Continuum Mechanics and Mathematical Physics for Nonclassical
Domains," Dokl. Ross. Akad. Nauk
284 (1), 73-76 (1985)
[Dokl. Phys. (Engl. transl.)]. |
| 12. | A. Norris,
"Dynamic Green's Functions in Anisotropic Piezoelectric, Thermoelastic,
and Poroelastic Solids,"
Proc. Roy. Soc. London. A
447 (1929), 475-188 (1994). |
| 13. | A. V. Amenitskii, L. A. Igumnov, and I. S. Karelin,
"Development of the Boundary Element Method for Solving the Problems
of Wave Propagation in Porous Media,"
Probl. Prochn. Plastichn.
70, 71-78 (2008). |
| 14. | A. V. Amenitskii, A. A. Belov, L. A. Igumnov, and I. S. Karelin,
"Boundary Integral Equations for Solving Dynamic Problems
of Three-Dimensional Theory of Poroelasticity,"
Probl. Prochn. Plastichn.
71, 164-171 (2009). |
| 15. | L. A. Igumnov,
"Boundary Integral Equations for Three-Dimensional Problems on Plane Waves,"
Dokl. Ross. Akad. Nauk
409 (5), 622-626 (2006)
[Dokl. Phys. (Engl. transl.)
51 (8), 440-443 (2006)]. |
| 16. | A. O. Vatul'yan,
"On Boundary Integral Equations of the First Kind in Dynamic Problems
of Anisotropic Elasticity,"
Dokl. Ross. Akad. Nauk
333 (3), 312-314 (1993)
[Dokl. Phys. (Engl. transl.)]. |
|
| Received |
23 May 2016 |
| Link to Fulltext |
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