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 par- tial 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 sys- tem 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 general- ized α-method illustrating the computational efficiency of our approach for problems in structural mechanics.
Bibtex
@INPROCEEDINGS{LyakhovGerdtWeberMichels2017, author = {Lyakhov, Dmitry A. and Gerdt, Vladimir P. and Weber, Andreas and Michels, Dominik L.}, pages = {301--312}, title = {Symbolic-Numeric Integration of the Dynamical Cosserat Equations}, booktitle = {Computer Algebra in Scientific Computing (CASC 2017)}, series = {Lecture Notes in Computer Science}, volume = {10490}, year = {2017}, publisher = {Spring}, location = {Beijing, China}, abstract = {We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear par- tial 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 sys- tem 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 general- ized α-method illustrating the computational efficiency of our approach for problems in structural mechanics.}, url = {http://link.springer.com/10.1007/978-3-319-45641-6}, doi = {10.1007/978-3-319-66320-3 22} }