Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics by Peter Betsch

Author:Peter Betsch
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Starting values according to (141) satisfy assumption (137) with since . Hence, Theorem 4.18(b) proves second-order convergence of the stabilized index-2 integrator (56) for all solution components. This convergence result may be verified by a numerical test for the heavy top benchmark problem in configuration space : Fig. 16 shows for time step size the global error of the stabilized index-2 integrator (56) in time interval [0, 0.1]. The test results in the left plot are already known from the left plot of Fig. 13. They show the transient oscillating first-order error term being characteristic of the trivial initialization . The test results in the right plot illustrate that this first-order error term disappears if we use the modified starting value .

Fig. 17Heavy top benchmark (, starting values , , index-3 formulation, ): Global error . Left plot , right plot

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