A new conservative/dissipative time integration scheme for nonlinear mechanical systems

authored by: Cristian Guillermo Gebhardt, Ignacio Romero, Raimund Rolfes
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.
Organisation(s): Institute of Structural Analysis
External Organisation(s): IMDEA Materials Institute
Technical University of Madrid (UPM)
Type: Article
Journal: Computational mechanics
Volume: 65
Pages: 405-427
No. of pages: 23
ISSN: 0178-7675
Publication date: 02.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, 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://arxiv.org/abs/1903.08728 (Access: Open)
https://doi.org/10.1007/s00466-019-01775-3 (Access: Closed)