On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics

[+] Author and Article Information
T. Belytschko, D. F. Schoeberle

Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.

J. Appl. Mech 42(4), 865-869 (Dec 01, 1975) (5 pages) doi:10.1115/1.3423721 History: Received November 01, 1974; Revised April 01, 1975; Online July 12, 2010


In this paper an implicit Newmark β-method with iterations for nonlinear structural dynamics is described; the algorithm is identical to standard algorithms except that a new convergence criterion is employed. A discrete energy is defined and it is shown that this discrete energy is bounded regardless of the size of the time step; this is a sufficient condition for the unconditional stability of the algorithm for nonlinear material problems. Numerical examples are given for problems with both geometric and material nonlinearities.

Copyright © 1975 by ASME
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