The stability of numerical time integrators, and of the physical systems to which they are applied, are normally studied independently. This conceals a very interesting phenomenon, here termed inconsistent stability, wherein a numerical time marching scheme predicts a stable response about an equilibrium configuration that is, in fact, unstable. In this paper, time integrator parameters leading to possible inconsistent stability are first found analytically for conservative systems (symmetric tangent stiffness matrices), then several structural arches with increasing complexity are used as numerical case studies. The intention of this work is to highlight the potential for this unexpected, and mostly unknown, behavior to researchers studying complex dynamical systems, especially through time marching of finite element models. To allow for direct interpretation of our results, the work is focused on the Newmark time integrator, which is commonly used in structural dynamics.
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September 2015
Research-Article
Inconsistent Stability of Newmark's Method in Structural Dynamics Applications
Richard Wiebe,
Richard Wiebe
1
1Present address: University of Washington, 201 More Hall, Box 352700, Seattle, WA 98195-2700
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Ilinca Stanciulescu
e-mail: ilinca.s@rice.edu
Ilinca Stanciulescu
2
Rice University
,208 Ryon Laboratory, MS 318
,6100 Main Street, Houston, TX 77005
e-mail: ilinca.s@rice.edu
2Corresponding author.
Search for other works by this author on:
Richard Wiebe
Ilinca Stanciulescu
Rice University
,208 Ryon Laboratory, MS 318
,6100 Main Street, Houston, TX 77005
e-mail: ilinca.s@rice.edu
1Present address: University of Washington, 201 More Hall, Box 352700, Seattle, WA 98195-2700
2Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 27, 2014; final manuscript received August 5, 2014; published online April 2, 2015. Assoc. Editor: Dan Negrut.
J. Comput. Nonlinear Dynam. Sep 2015, 10(5): 051006 (8 pages)
Published Online: September 1, 2015
Article history
Received:
February 27, 2014
Revision Received:
August 5, 2014
Online:
April 2, 2015
Citation
Wiebe, R., and Stanciulescu, I. (September 1, 2015). "Inconsistent Stability of Newmark's Method in Structural Dynamics Applications." ASME. J. Comput. Nonlinear Dynam. September 2015; 10(5): 051006. https://doi.org/10.1115/1.4028221
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