Symbolic-Numeric Integration of the Dynamical Cosserat Equations
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We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \(\alpha \)-method illustrating the computational efficiency of our approach for problems in structural mechanics.
KeywordsAnalytical solution Cosserat rods Dynamic equations Exponential integration Generalized \(\alpha \)-method Kinematic equations Symbolic computation
The authors appreciate the insightful comments of the anonymous referees. This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline funding), the Max Planck Center for Visual Computing and Communication (MPC-VCC) funded by Stanford University and the Federal Ministry of Education and Research of the Federal Republic of Germany (BMBF grants FKZ-01IMC01 and FKZ-01IM10001), the Russian Foundation for Basic Research (grant 16-01-00080) and the Ministry of Education and Science of the Russian Federation (agreement 02.a03.21.0008).
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