Symbolic-Numeric Integration of the Dynamical Cosserat Equations

Handle URI:
http://hdl.handle.net/10754/626006
Title:
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Authors:
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.
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.
KAUST Department:
Visual Computing Center (VCC)
Citation:
Lyakhov DA, Gerdt VP, Weber AG, Michels DL (2017) Symbolic-Numeric Integration of the Dynamical Cosserat Equations. Lecture Notes in Computer Science: 301–312. Available: http://dx.doi.org/10.1007/978-3-319-66320-3_22.
Publisher:
Springer International Publishing
Journal:
Computer Algebra in Scientific Computing
Conference/Event name:
19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017
Issue Date:
29-Aug-2017
DOI:
10.1007/978-3-319-66320-3_22
Type:
Conference Paper
ISSN:
0302-9743; 1611-3349
Sponsors:
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).
Additional Links:
https://link.springer.com/chapter/10.1007%2F978-3-319-66320-3_22
Appears in Collections:
Conference Papers; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorLyakhov, Dmitry A.en
dc.contributor.authorGerdt, Vladimir P.en
dc.contributor.authorWeber, Andreas G.en
dc.contributor.authorMichels, Dominik L.en
dc.date.accessioned2017-10-30T08:39:50Z-
dc.date.available2017-10-30T08:39:50Z-
dc.date.issued2017-08-29en
dc.identifier.citationLyakhov DA, Gerdt VP, Weber AG, Michels DL (2017) Symbolic-Numeric Integration of the Dynamical Cosserat Equations. Lecture Notes in Computer Science: 301–312. Available: http://dx.doi.org/10.1007/978-3-319-66320-3_22.en
dc.identifier.issn0302-9743en
dc.identifier.issn1611-3349en
dc.identifier.doi10.1007/978-3-319-66320-3_22en
dc.identifier.urihttp://hdl.handle.net/10754/626006-
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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).en
dc.publisherSpringer International Publishingen
dc.relation.urlhttps://link.springer.com/chapter/10.1007%2F978-3-319-66320-3_22en
dc.subjectAnalytical solutionen
dc.subjectCosserat rodsen
dc.subjectDynamic equationsen
dc.subjectExponential integrationen
dc.subjectGeneralized α-methoden
dc.subjectKinematic equationsen
dc.subjectSymbolic computationen
dc.titleSymbolic-Numeric Integration of the Dynamical Cosserat Equationsen
dc.typeConference Paperen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalComputer Algebra in Scientific Computingen
dc.conference.date2017-09-18 to 2017-09-22en
dc.conference.name19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017en
dc.conference.locationBeijing, CHNen
dc.contributor.institutionPeoples’ Friendship University of Russia, 6 Miklukho–Maklaya St., Moscow, 117198, , Russian Federationen
dc.contributor.institutionLaboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot–Curie St., Dubna, 141980, , Russian Federationen
dc.contributor.institutionInstitute of Computer Science II, University of Bonn, Friedrich-Ebert-Allee 144, Bonn, 53113, , Germanyen
dc.contributor.institutionDepartment of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA, 94305, , United Statesen
kaust.authorLyakhov, Dmitry A.en
kaust.authorMichels, Dominik L.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.