Abstract
Various methods for solving systems of differential-algebraic equations (DAE), e.g. constrained mechanical systems, are known from literature. Here, an alternative approach is suggested, which is called collocated constraints approach (CCA). The idea of the method is inspired by a co-simulation technique recently published in [11] and is based on the usage of intermediate time points. The approach is very general and can basically be applied for arbitrary DAE systems. In the paper at hand, implementations of this approach are presented for Newmark-type integration schemes [1, 9, 12]. We discuss index-2 formulations with one intermediate time point and index-1 implementations based on two intermediate time points. A direct application of the approach for Newmark-type integrators yields a system of discretized equations with larger dimensions. Roughly speaking, the system increases by factor 2 for the index-2 and by factor 3 in case of the index-1 formulation. It is, however, straightforward to reduce the size of the discretized DAE system by using simple interpolation techniques. Numerical examples will demonstrate the straightforward application of the approach.
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Meyer, T., Li, P., Schweizer, B. (2020). Alternative Integration Schemes for Constrained Mechanical Systems. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_38
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DOI: https://doi.org/10.1007/978-3-030-23132-3_38
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