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Geometrically exact beam equations in the adaptive DCA framework

Part 1: Static example

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Abstract

This work examines the suitability of two popular methods of modeling bodies that undergo large deformation for use in the adaptive divide-and-conquer framework. In this framework, the method used to form and solve the equations-of-motion must handle a mixed set of bodies using different formulations, such as rigid-bodies that use a Newton–Euler formulation or flexible-bodies that use a floating frame of reference. Importantly, the method must treat all bodies indiscriminately of underlying formulation since the goal is to have adaptive changes in body definition, e.g., various rigid-bodies to a highly-flexible body. This work shows that the absolute nodal coordinate formulation is not immediately suitable for this purpose and derives the geometrically exact beam formulation equations that are compatible with these adaptive changes in body definition.

An example problem that demonstrates the accuracy of this work is presented for the static case since the solution is known analytically and can be used for comparison. This work lays the foundation for adaptive changes in body definition because the DCA can now deal with bodies that are rigid, flexible, and highly-flexible, indiscriminately. Furthermore, using the DCA to solve the equations-of-motion for systems of mixed body types, some of which undergo large deformations, does not require the rigid or FFR body to be discretized, as would be necessary with some software packages using finite element method type approach. This greatly reduces the number of degrees-of-freedom and therefore the computational effort required to simulate such systems.

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Acknowledgements

This work was completed under grant 1161872 from the National Science Foundation and the authors are grateful for this support.

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Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Jeremy J. Laflin

  2. Department of Mechanical, Aerospace, and Nuclear, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Kurt S. Anderson

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Correspondence to Jeremy J. Laflin.

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Laflin, J.J., Anderson, K.S. Geometrically exact beam equations in the adaptive DCA framework. Multibody Syst Dyn 47, 1–19 (2019). https://doi.org/10.1007/s11044-019-09669-1

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