A path following method for identifying static equilibrium in multi-body-dynamic systems
Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static solvers. Analysts are often faced with uncertainty in regards to the values of candidate equilibrium states or whether a state of minimum potent...
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Published in | Multibody system dynamics Vol. 45; no. 3; pp. 315 - 359 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
15.03.2019
Springer Nature B.V |
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Abstract | Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static solvers. Analysts are often faced with uncertainty in regards to the values of candidate equilibrium states or whether a state of minimum potential energy was found. In the event of static solver failure or uncertainty with regards to a candidate solution, equilibrium could be obtained through a dynamic simulation which may require the addition of artificial damping. However, this method can have significant computational expense as compared to static solution procedures. Using MBD systems representing a pendulum, two variations of a spring supported arch, and a seven-body mechanism, arc-length solvers were found suitable for identifying equilibrium states through a robust production of static solution curves thereby avoiding dynamic simulation. Using these examples, a procedure for finding the correct equilibrium state for general systems is proposed. |
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AbstractList | Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static solvers. Analysts are often faced with uncertainty in regards to the values of candidate equilibrium states or whether a state of minimum potential energy was found. In the event of static solver failure or uncertainty with regards to a candidate solution, equilibrium could be obtained through a dynamic simulation which may require the addition of artificial damping. However, this method can have significant computational expense as compared to static solution procedures. Using MBD systems representing a pendulum, two variations of a spring supported arch, and a seven-body mechanism, arc-length solvers were found suitable for identifying equilibrium states through a robust production of static solution curves thereby avoiding dynamic simulation. Using these examples, a procedure for finding the correct equilibrium state for general systems is proposed. |
Author | Rose, Geoffrey K. Newman, Brett A. Nguyen, Duc T. |
Author_xml | – sequence: 1 givenname: Geoffrey K. orcidid: 0000-0001-7567-2598 surname: Rose fullname: Rose, Geoffrey K. email: geoffrey.k.rose@nasa.gov organization: Structural Dynamics Branch, NASA Langley Research Center – sequence: 2 givenname: Brett A. surname: Newman fullname: Newman, Brett A. organization: Department of Mechanical and Aerospace Engineering, Old Dominion University – sequence: 3 givenname: Duc T. surname: Nguyen fullname: Nguyen, Duc T. organization: Department of Civil and Environmental Engineering, Old Dominion University |
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Keywords | Multi-body-dynamics Nonlinear equations Arc-length method Path following |
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References_xml | – year: 2016 ident: CR1 article-title: Implementing an arc-length method for a robust approach in solving systems of nonlinear equations publication-title: IEEE Southeast Conference contributor: fullname: Newman – year: 1990 ident: CR15 publication-title: Multibody Systems Handbook doi: 10.1007/978-3-642-50995-7 contributor: fullname: Schiehlen – ident: CR22 – year: 1981 ident: CR19 article-title: Strategies for tracing the nonlinear response near limit points publication-title: Proceedings of the Europe–U.S. Workshop on Nonlinear Finite Element Analysis in Structural Mechanics contributor: fullname: Ramm – start-page: 3 year: 1997 end-page: 207 ident: CR9 article-title: Numerical path following publication-title: Handbook of Numerical Analysis, Vol. V. 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Snippet | Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static... |
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SubjectTerms | Arches Automotive Engineering Computer simulation Control Damping Dynamical Systems Electrical Engineering Engineering Equilibrium Failure analysis Mechanical Engineering Nonlinear analysis Optimization Potential energy Robustness (mathematics) Solvers Static equilibrium Trajectory planning Uncertainty Vibration |
Title | A path following method for identifying static equilibrium in multi-body-dynamic systems |
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