Static equations for thin inextensible elastic rods, or elastica as they are sometimes called, have been studied since before the time of Euler. In this paper, we examine how to model the dynamic behavior of elastica. We present a fairly high speed, robust numerical scheme that uses (i) a space discretization that uses cubic splines, and (ii) a time discretization that preserves a discrete version of the Hamiltonian. A good choice of numerical scheme is important because these equations are very stiff; that is, most explicit numerical schemes will become unstable very quickly. The authors conducted this research anticipating describing the dynamic Kirchhoff problem, that is, the behavior of general springs that have natural curvature, and for which the equations take into account torsion of the rod.
A Numerical Method to Model Dynamic Behavior of Thin Inextensible Elastic Rods in Three Dimensions
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 25, 2012; final manuscript received October 1, 2013; published online November 7, 2013. Assoc. Editor: Johannes Gerstmayr.
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Montgomery-Smith, S., and Huang, W. (November 7, 2013). "A Numerical Method to Model Dynamic Behavior of Thin Inextensible Elastic Rods in Three Dimensions." ASME. J. Comput. Nonlinear Dynam. January 2014; 9(1): 011015. https://doi.org/10.1115/1.4025627
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