Symbolic-Numeric Integration of the Dynamical Cosserat Equations

Dmitry Lyakhov; Vladimir P. Gerdt; Andreas G. Weber; Dominik L. Michels

doi:10.1007/978-3-319-66320-3_22

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

Dmitry Lyakhov, Vladimir P. Gerdt, Andreas G. Weber, Dominik L. Michels

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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.

Original language	English (US)
Title of host publication	Computer Algebra in Scientific Computing
Publisher	Springer Nature
Pages	301-312
Number of pages	12
ISBN (Print)	9783319663197
DOIs	https://doi.org/10.1007/978-3-319-66320-3_22
State	Published - Aug 30 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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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title = "Symbolic-Numeric Integration of the Dynamical Cosserat Equations",

abstract = "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.",

author = "Dmitry Lyakhov and Gerdt, {Vladimir P.} and Weber, {Andreas G.} and Michels, {Dominik L.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).",

year = "2017",

month = aug,

day = "30",

doi = "10.1007/978-3-319-66320-3_22",

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AU - Lyakhov, Dmitry

AU - Gerdt, Vladimir P.

AU - Weber, Andreas G.

AU - Michels, Dominik L.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).

PY - 2017/8/30

Y1 - 2017/8/30

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/626006

UR - https://link.springer.com/chapter/10.1007%2F978-3-319-66320-3_22

UR - http://www.scopus.com/inward/record.url?scp=85029795538&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66320-3_22

DO - 10.1007/978-3-319-66320-3_22

M3 - Conference contribution

SN - 9783319663197

SP - 301

EP - 312

BT - Computer Algebra in Scientific Computing

PB - Springer Nature

ER -

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

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