On implicit methods for integration of parameterized equations of nonlinear dynamic system

Аuthors

Danilin A. N.^*, Volkov-Bogorodsky D. B.

Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia

*e-mail: andanilin@yandex.ru

Abstract

It is possible to develop simple and effective implicit numerical step-by-step integration procedure to solve nonlinear second-order ordinary differential equations with respect to the length of integral curve. This procedure does not contain time-consuming iterative processes. An implicit algorithm proposed bases on the linear acceleration scheme with simple iterations only. Unique existence theorems for equation solution are proved as well as convergence conditions for corresponding iterative process. The technique offered can be applied to nonlinear dynamical simulation for strained systems. An example problem is considered for highly nonlinear strain of elastic flexible cantilever bar. The bar is coiled into a ring initially due to external bending moment. The problem is stated in finite-element form and it is solved using the best parameterization procedure.