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.
Inconsistent Stability of Newmark's Method in Structural Dynamics Applications
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.
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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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