An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity

Part 2: shells

authored by: E. M.B. Campello, P. M. Pimenta, P. Wriggers
Abstract: Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computational mechanics
Volume: 48
Pages: 195-211
No. of pages: 17
ISSN: 0178-7675
Publication date: 30.03.2011
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Sustainable Development Goals: SDG 7 - Affordable and Clean Energy
Electronic version(s): https://doi.org/10.1007/s00466-011-0584-7 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{7e4b5f75d299459fa03a151d8fa15f0f,
title = "An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity: Part 2: shells",
abstract = "Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.",
keywords = "Energy conservation, Momentum conservation, Nonlinear dynamics, Shells, Time integration",
author = "Campello, {E. M.B.} and Pimenta, {P. M.} and P. Wriggers",
year = "2011",
month = mar,
day = "30",
doi = "10.1007/s00466-011-0584-7",
language = "English",
volume = "48",
pages = "195--211",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "2",
}