Details
| Original language | English |
|---|---|
| Pages (from-to) | 195-211 |
| Number of pages | 17 |
| Journal | Computational mechanics |
| Volume | 48 |
| Issue number | 2 |
| Publication status | Published - 30 Mar 2011 |
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
ASJC Scopus subject areas
- 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. 48, No. 2, 30.03.2011, p. 195-211.
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
T2 - Part 2: shells
AU - Campello, E. M.B.
AU - Pimenta, P. M.
AU - Wriggers, P.
PY - 2011/3/30
Y1 - 2011/3/30
N2 - 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.
AB - 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.
KW - Energy conservation
KW - Momentum conservation
KW - Nonlinear dynamics
KW - Shells
KW - Time integration
UR - http://www.scopus.com/inward/record.url?scp=80052651128&partnerID=8YFLogxK
U2 - 10.1007/s00466-011-0584-7
DO - 10.1007/s00466-011-0584-7
M3 - Article
AN - SCOPUS:80052651128
VL - 48
SP - 195
EP - 211
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 2
ER -