An Improved Stiffly Stable Method for Direct Integration of Nonlinear Structural Dynamic Equations

[+] Author and Article Information
K. C. Park

Structural Mechanics Laboratory, Lockheed Palo Alto Research Laboratory, Palo Alto, Calif.

J. Appl. Mech 42(2), 464-470 (Jun 01, 1975) (7 pages) doi:10.1115/1.3423600 History: Received August 01, 1974; Revised November 01, 1974; Online July 12, 2010


The behavior of linear multistep methods has been evaluated for application to structural dynamics problems. By examining the local stability of the currently popular methods as applied to nonlinear problems, it is shown that the presence of historical derivatives can cause numerical instability in the nonlinear dynamics even for methods that are unconditionally stable for linear problems. Through an understanding of the stability characteristics of Gear’s two-step and three-step methods, a new method requiring no historical derivative information has been developed. Superiority of the new method for nonlinear problems is indicated by means of comparisons with currently popular methods.

Copyright © 1975 by ASME
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