Geodesic
A comparative analysis of methods for solving equations in the nonlinear elasticity theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2013), pp. 61-65 
M. V. Kozlov; S. V. Sheshenin. A comparative analysis of methods for solving equations in the nonlinear elasticity theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2013), pp. 61-65. http://geodesic.mathdoc.fr/item/VMUMM_2013_4_a13/
@article{VMUMM_2013_4_a13,
     author = {M. V. Kozlov and S. V. Sheshenin},
     title = {A comparative analysis of methods for solving equations in the nonlinear elasticity theory},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--65},
     year = {2013},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_4_a13/}
}
TY  - JOUR
AU  - M. V. Kozlov
AU  - S. V. Sheshenin
TI  - A comparative analysis of methods for solving equations in the nonlinear elasticity theory
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2013
SP  - 61
EP  - 65
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2013_4_a13/
LA  - ru
ID  - VMUMM_2013_4_a13
ER  - 
%0 Journal Article
%A M. V. Kozlov
%A S. V. Sheshenin
%T A comparative analysis of methods for solving equations in the nonlinear elasticity theory
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2013
%P 61-65
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2013_4_a13/
%G ru
%F VMUMM_2013_4_a13

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

In this paper we describe the way of practical solution of the variational equation in geometrically and physically nonlinear problems of deformable body mechanics. A system of a large number of nonlinear ordinary differential equations usually appears in such problems. The Euler method is typically used in this approach. We propose to use a Runge–Kutta method and multistep methods and consider the solution complexity in terms of computing cost to find a method that provides a more efficient solving procedure of nonlinear problems.

[1] Bonet J., Wood R., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge Univ. Press, Cambridge, 1997 | MR

[2] Pobedrya B.E., Chislennye metody v teorii uprugosti i plastichnosti, Izd-vo MGU, M., 1995 | MR

[3] Zenkevich O., Metod konechnykh elementov v tekhnike, Mir, M., 1975

[4] Kelley C.T., Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995 | MR

[5] Memon B.A., Su X.Z., “Arc-length technique for nonlinear finite element analysis”, J. Zhejiang Univ. SCI., 5:5 (2004), 618–628 | DOI

[6] Butcher J.C., Numerical Methods for Ordinary Differential Equations, John Wiley Sons, Chichester, 2008 | MR