Abstract The application of the Petrov--Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity-free formulation.
%0 Journal Article
%1 Harsch2023b
%A Harsch, Jonas
%A Eugster, Simon R.
%D 2023
%J PAMM
%K eugster inm journal project_harsch
%P e202300172
%R https://doi.org/10.1002/pamm.202300172
%T Nonunit quaternion parametrization of a Petrov--Galerkin Cosserat rod finite element
%U https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202300172
%X Abstract The application of the Petrov--Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity-free formulation.
@article{Harsch2023b,
abstract = {Abstract The application of the Petrov--Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity-free formulation.},
added-at = {2023-10-18T09:06:08.000+0200},
author = {Harsch, Jonas and Eugster, Simon R.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/24a4317091d10643291a87a93e40f985d/jharsch},
doi = {https://doi.org/10.1002/pamm.202300172},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.202300172},
interhash = {3e96b44541fc920eec4f3ff9a1cc128f},
intrahash = {4a4317091d10643291a87a93e40f985d},
journal = {PAMM},
keywords = {eugster inm journal project_harsch},
pages = {e202300172},
timestamp = {2023-10-18T09:06:08.000+0200},
title = {Nonunit quaternion parametrization of a Petrov--Galerkin Cosserat rod finite element},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202300172},
year = 2023
}