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We present and evaluate the formulation of a reduced-dimension (one-dimensional) finite element for the nonlinear analysis of a vibrating disk in a two-dimensional unbounded domain. As this problem is relevant in studies of the dynamic response of laterally loaded piles, numerous spring-and-dashpot representations of the disk undergoing displacement in an unbounded material domain have been developed to date: static and dynamic, linear and nonlinear. With the focus on material nonlinearity, the present simplified formulation circumvents the complications associated with nonlinear springs and dashpots. Indeed, the continuum-based treatment described herein accounts for the interaction between the two modes of energy dissipation, due to wave propagation in the unbounded domain and loss associated with inelastic behavior. The formulation is a good compromise between the competing desires for realistic representation and efficient computation. Copyright © 2011 John Wiley & Sons, Ltd. |
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