Symbolic-Numeric Integration of the Dynamical Cosserat Equations

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. © 2017, Springer International Publishing AG.

Авторы
Lyakhov D.A.1 , Gerdt V.P. 3, 4 , Weber A.G.5 , Michels D.L.1, 2
Язык
Английский
Страницы
301-312
Статус
Опубликовано
Том
10490 LNCS
Год
2017
Организации
  • 1 Visual Computing Center, King Abdullah University of Science and Technology, Al Khawarizmi Building, Thuwal, 23955-6900, Saudi Arabia
  • 2 Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA 94305, United States
  • 3 Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot–Curie St., Dubna, 141980, Russian Federation
  • 4 Peoples’ Friendship University of Russia, 6 Miklukho–Maklaya St., Moscow, 117198, Russian Federation
  • 5 Institute of Computer Science II, University of Bonn, Friedrich-Ebert-Allee 144, Bonn, 53113, Germany
Ключевые слова
Analytical solution; Cosserat rods; Dynamic equations; Exponential integration; Generalized α-method; Kinematic equations; Symbolic computation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6281/
Поделиться

Другие записи