Details
| Original language | English |
|---|---|
| Pages (from-to) | 715-732 |
| Number of pages | 18 |
| Journal | Computational mechanics |
| Volume | 42 |
| Issue number | 5 |
| Publication status | Published - 2 Apr 2008 |
Abstract
A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.
Keywords
- Energy conservation, Momentum conservation, Nonlinear dynamics, Rods, Time integration
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Sustainable Development Goals
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In: Computational mechanics, Vol. 42, No. 5, 02.04.2008, p. 715-732.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1
T2 - Rods
AU - Pimenta, P. M.
AU - Campello, E. M.B.
AU - Wriggers, Peter
PY - 2008/4/2
Y1 - 2008/4/2
N2 - A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.
AB - A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.
KW - Energy conservation
KW - Momentum conservation
KW - Nonlinear dynamics
KW - Rods
KW - Time integration
UR - http://www.scopus.com/inward/record.url?scp=47849128642&partnerID=8YFLogxK
U2 - 10.1007/s00466-008-0271-5
DO - 10.1007/s00466-008-0271-5
M3 - Article
AN - SCOPUS:47849128642
VL - 42
SP - 715
EP - 732
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 5
ER -