Geodesic
Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images
Matematičeskoe modelirovanie, Tome 26 (2014) no. 1, pp. 109-121.

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

Meshless method of the mathematical simulation of the dynamics of the three-dimensional nonlinearly deformed hyperelastic media, based on the Hamiltonian description of discrete classical mechanics and symplectic integration method for the solution on the temporary layer is developed. The comparative results of solution of model problem and the solution of the actual problem of biomechanics about the dynamics of the artificial valve of heart are represented.
Keywords: biomechanics, deformable media, finite deformation, point approximation, Hamiltonian description, symplectic integrator, mathematical simulation. 
@article{MM_2014_26_1_a8,
     author = {A. I. Nadaryshvili and V. A. Petushkov},
     title = {Simulation of nonlinear dynamics of {Hamiltonian} systems in biomechanics using computed tomography images},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {109--121},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/}
}
TY  - JOUR
AU  - A. I. Nadaryshvili
AU  - V. A. Petushkov
TI  - Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images
JO  - Matematičeskoe modelirovanie
PY  - 2014
SP  - 109
EP  - 121
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/
LA  - ru
ID  - MM_2014_26_1_a8
ER  - 
%0 Journal Article
%A A. I. Nadaryshvili
%A V. A. Petushkov
%T Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images
%J Matematičeskoe modelirovanie
%D 2014
%P 109-121
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/
%G ru
%F MM_2014_26_1_a8
A. I. Nadaryshvili; V. A. Petushkov. Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images. Matematičeskoe modelirovanie, Tome 26 (2014) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/

[1] Belystchko T., Krongauz Y., Organ D., Fleming M., Krys P., “Meshless methods: An overview and recent developments”, Comput. Methods in Appl. Mech. Eng., 139 (1996), 3–47 | DOI

[2] Zabrodin A. V., “Super EVM MVS-100, MVS-1000 i opyt ikh ispolzovaniya pri reshenii zadach mekhaniki i fiziki”, Matematicheskoe modelirovanie, 12:5 (2000), 61–66

[3] Arnold V. I., Kozlov V. V., Neishtadt A. I., “Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki”, Dinamicheskie sistemy – 3, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. Napravleniya, 3, VINITI, M., 1985, 5–290

[4] Leimkuhler B., Reich S., Simulating Hamiltonian Dynamics, Cambridge Univ. Press, Cambridge, 2004, 379 pp. | MR | Zbl

[5] Lancaster P., Salkauskas K., “Surfaces generated by moving least squares methods”, Mathematics of Computation, 37 (1981), 141–158 | DOI | MR | Zbl

[6] Liu H., Shi P., “Meshfree Particle Method”, Proc. of the Ninth IEEE International Conference on Computer Vision (ICCV 2003), IEEE Computer Society, 2003, 1–8

[7] Trusdell K., Pervonachalnyi kurs ratsionalnoi mekhaniki sploshnykh sred, Mir, M., 1975, 592 pp.

[8] Taber L. A., Nonlinear theory of elasticity — applications in biomechanics, World Scientific, London, 2004, 416 pp. | Zbl

[9] de Berg M., Cheong O., van Kreveld M., Overmars M., Algorithms and Applications, Computational Geometry, 3rd ed., Springer, 2008, 386 pp. | MR

[10] MATLAB 7, The MathWorks Web Site Resources, 2009

[11] Nadareyshvili A. I., Chandran K. B., Lu Jia, “Image-based point cloud Hamiltonian dynamic analysis for biomechanical systems”, Intern. J. for Numerical Methods in Biomedical Engineering, 27 (2011), 1507–1523 | DOI | MR | Zbl

[12] Marsden J. E., Patrick G. W., Shadwick W. F. (eds.), Integration Algorithms and Classical Mechanics, AMS, Fields Institute Communications, 1996, 244 pp. | MR | Zbl

[13] Simo J. C., Tarnow N., Wong K. K., “Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics”, Comput. Methods Appl. Mech. Eng., 100 (1992), 63–116 | DOI | MR | Zbl

[14] Kondo M., Koshizuka S., Suzuki Y., “Application of symplectic scheme to three-dimensional elastic analysis using MPS method”, Trans. of the Japan Society of Mech. Eng., Part A, 72 (2006), 425–431 | DOI