Details
| Original language | English |
|---|---|
| Pages (from-to) | 405-427 |
| Number of pages | 23 |
| Journal | Computational mechanics |
| Volume | 65 |
| Issue number | 2 |
| Early online date | 12 Oct 2019 |
| Publication status | Published - Feb 2020 |
Abstract
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples.
Keywords
- Conservative/dissipative time integration scheme, Linearly constrained quadratic programs, Nonlinear mechanical systems, Optimality conditions, Unconditional energy stability
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. 65, No. 2, 02.2020, p. 405-427.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new conservative/dissipative time integration scheme for nonlinear mechanical systems
AU - Gebhardt, Cristian Guillermo
AU - Romero, Ignacio
AU - Rolfes, Raimund
N1 - Funding information: Cristian Guillermo Gebhardt and Raimund Rolfes acknowledge the financial support of the Lower Saxony Ministry of Science and Culture (research project ventus efficiens, FKZ ZN3024) and the German Federal Ministry for Economic Affairs and Energy (research project Deutsche Forschungsplattform für Windenergie, FKZ 0325936E) that enabled this work.
PY - 2020/2
Y1 - 2020/2
N2 - We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples.
AB - We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples.
KW - Conservative/dissipative time integration scheme
KW - Linearly constrained quadratic programs
KW - Nonlinear mechanical systems
KW - Optimality conditions
KW - Unconditional energy stability
UR - http://www.scopus.com/inward/record.url?scp=85074019457&partnerID=8YFLogxK
U2 - 10.1007/s00466-019-01775-3
DO - 10.1007/s00466-019-01775-3
M3 - Article
AN - SCOPUS:85074019457
VL - 65
SP - 405
EP - 427
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 2
ER -