Comparative analysis of integration methods for nonlinear elasticity theory equations / M. V. Kozlov, S. V. Sheshenin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 4. P. 61-65 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
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.
Key words: rubber-cord, composite, nonlinearity, variational equation, linearization, finite element method, Euler method, Newton method, Runge-Kutta method, multistep method.