Geodesic
Finite difference schemes for problems of mixture of two component elastic materials
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 109-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the numerical approximation of the solution of the 2D unsteady equations of mixture on a rectangular domain using the operator-splitting schemes for solving unsteady elasticity problems. Its major peculiarity is that transition to the next time level is performed by solving separate elliptic problems for each component of the displacement vector. The previous results make it possible to design efficient numerical algorithms for two component mixture elasticity equations. 
@article{BASM_2006_3_a10,
     author = {Ghenadie Bulgac},
     title = {Finite difference schemes for problems of mixture  of two component elastic materials},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {109--116},
     publisher = {mathdoc},
     number = {3},
     year = {2006},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2006_3_a10/}
}
TY  - JOUR
AU  - Ghenadie Bulgac
TI  - Finite difference schemes for problems of mixture  of two component elastic materials
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2006
SP  - 109
EP  - 116
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2006_3_a10/
LA  - en
ID  - BASM_2006_3_a10
ER  - 
%0 Journal Article
%A Ghenadie Bulgac
%T Finite difference schemes for problems of mixture  of two component elastic materials
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2006
%P 109-116
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2006_3_a10/
%G en
%F BASM_2006_3_a10
Ghenadie Bulgac. Finite difference schemes for problems of mixture  of two component elastic materials. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 109-116. https://geodesic-test.mathdoc.fr/item/BASM_2006_3_a10/

[1] Steel T. R., “Applications of a theory of interacting continua”, Quart. J. Mech. and Appl. Math., 20:1 (1967), 57–72 | DOI | Zbl

[2] Steel T. R., “Linearized theory of plane strain of mixture of two solids”, Int. J. Eng. Scienc., 5:10 (1967), 775–790 | DOI

[3] Basheleishvili M. O., “Two-Dimensional Boundary Value Problems of Statics of the Elastic Mixtures”, Memories on Diff. Eq. and Math. Physics, 6, Tbilisi, 1995, 59–105 | MR | Zbl

[4] Natroshvili D. G., Jagmaidze A. J., Svanadze M. Zh., Some problems of the theory of elastic mixtures, Tbilisi Univ. Press, Tbilisi, 1986 (in Russian)

[5] Samarskii A. A., Vabishchevich P. N., Additive Schemes for Problems of Mathematical Physics, Nauka, Moskva, 1999 (in Russian) | MR

[6] Rushchitskii Ya. Ya., Elements of mixture theory, Naukova Dumka, Kiev, 1991 (in Russian) | MR

[7] Lempriere B., On practice ability of analyzing waves in composites by the theory of mixtures, Report No LMSC-6-78-69-21, Lockheed Palo Alto Research Laboratory, 1969, 76–90

[8] McNiven H. D., Mengi Y. A., “A mathematical model for the linear dynamic behavior of two-phase periodic materials”, Int. J. Solids and Struct., 15:4 (1979), 571–580 | MR

[9] Khoroshunand L. P., Soltanov N. S., Thermoelasticity of two-component mixtures, Naukova Dumka, Kiev, 1984 (in Russian)

[10] Filippov I. G., “Dynamical theory of a relative flow of multicomponent media”, Prikl. Mekhanika, 7:10 (1971), 92–99 (in Russian) | MR

[11] Samarskii A. A., “An economical algorithm for the numerical solution of system of differential and algebraic equations”, U.S.S.R. Comput. Math., Math. Phys., 4:3 (1964), 263–271 | DOI | MR | Zbl