| 11. |
- Arnold, Martin, et al.
(författare)
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Efficient corrector iteration for DAE time integration in multibody dynamics
- 2006
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 195:50-51, s. 6958-6973
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Tidskriftsartikel (refereegranskat)abstract
- Efficient time integration is a key issue in computational multibody dynamics. Implicit time integration methods for stiff systems and constrained systems require the solution of a system of nonlinear equations in each time step. The nonlinear equations are solved iteratively by Newton type methods that are tailored to the structure of the equations of motion in multibody dynamics. In the present paper we discuss classical and recent methods for reducing the numerical effort in the application to multibody systems that are modelled in joint coordinates. The methods have been implemented in an industrial multibody system simulation package. Results of numerical tests for two benchmark problems from vehicle dynamics are presented.
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| 12. |
- Arnold, Martin, et al.
(författare)
-
Numerical methods in vehicle system dynamics: state of the art and current developments
- 2011
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Ingår i: Vehicle System Dynamics. - : Informa UK Limited. - 1744-5159 .- 0042-3114. ; 49:7, s. 1159-1207
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Tidskriftsartikel (refereegranskat)abstract
- Robust and efficient numerical methods are an essential prerequisite for the computer based dynamical analysis of engineering systems. In vehicle system dynamics, the methods and software tools from multibody system dynamics provide the integration platform for the analysis, simulation and optimization of the complex dynamical behaviour of vehicles and vehicle components and their interaction with hydraulic components, electronical devices and control structures. Based on the principles of classical mechanics, the modelling of vehicles and their components results in nonlinear systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) of moderate dimension that describe the dynamical behaviour in the frequency range required and with a level of detail being characteristic of vehicle system dynamics. Most practical problems in this field may be transformed to generic problems of numerical mathematics like systems of nonlinear equations in the (quasi-)static analysis and explicit ODEs or DAEs with a typical semi-explicit structure in the dynamical analysis. This transformation to mathematical standard problems allows to use sophisticated, freely available numerical software that is based on well approved numerical methods like the Newton-Raphson iteration for nonlinear equations or Runge-Kutta and linear multistep methods for ODE/DAE time integration. Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics. In the present paper, we follow this framework and start with some modelling aspects being relevant from the numerical viewpoint. The focus of the paper is on numerical methods for static and dynamic problems including software issues and a discussion which method fits best for which class of problems. Adaptive components in state-of-the-art numerical software like stepsize and order control in time integration are introduced and illustrated by a well known benchmark problem from rail vehicle simulation. Over the last few decades, the complexity of high-end applications in vehicle system dynamics has frequently given a fresh impetus for substantial improvements of numerical methods and for the development of novel methods for new problem classes. In the present paper, we address three of these challenging problems of current interest that are today still beyond the mainstream of numerical mathematics: (i) Modelling and simulation of contact problems in multibody dynamics, (ii) Real-time capable numerical simulation techniques in vehicle system dynamics and iii) Modelling and time integration of multidisciplinary problems in system dynamics including co-simulation techniques.
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| 13. |
- Diaz, José, et al.
(författare)
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A wavelet semidiscretisation of elastic multibody systems
- 2003
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Ingår i: Zeitschrift für Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 83:10, s. 677-689
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider a coupled system of elastic and rigid bodies. It can be mathematically formulated as a coupled system of ordinary and partial differential equations, often written in its weak form. The discretisation is performed by a Galerkin-type ansatz in connection with a finite element approach or known eigenfunctions. Here, we demonstrate instead the use of a recently published Galerkin-wavelet method and its application to obtain a reasonable,small number of elastic modes.
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| 14. |
- Eich, Edda, et al.
(författare)
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On the error control for multistep methods applied to ODEs with invariants and DAEs in multibody dynamics
- 1995
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Ingår i: Mechanics of Structures and Machines. - : Informa UK Limited. - 0890-5452. ; 23:2, s. 159-180
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Tidskriftsartikel (refereegranskat)abstract
- A modified local error model is developed for numerical integration of ODEs with invariants. The basic idea is to use a commutativity relationship that holds for implicit state-space form methods. A new implicit state-space form predictor is developed from which error estimates can be obtained by predictor-corrector difference: This technique is demonstrated through the preliminary examples in this paper.
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| 15. |
- Eich, Edda, et al.
(författare)
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Stabilization and projection methods for multibody dynamics
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In recent years, there has been growing interest in stabilized index reduction techniques for differential-algebraic equations (DAE) of multibody dynamics. A number of the proposals which incorporate the idea of a projection onto the constraint manifold are discussed. The methods are divided into classes based on whether the projection is performed on the residuals of the discretized DAE or on the numerical solution itself, and demonstrate relationships between the methods of each class
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| 16. |
- Eich-Soellner, Edda, et al.
(författare)
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Numerische Methoden in der Mehrkörperdynamik
- 1995
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Ingår i: Mathematik in der Praxis: Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin. - 9783540592945 ; , s. 41-41
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Bokkapitel (populärvet., debatt m.m.)
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| 17. |
- Eichberger, Alex, et al.
(författare)
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The befenits of parallel multibody simulation and its application to vehicle dynamics
- 1993
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Ingår i: Advanced Multibody System Dynamics. - Dordrecht : Springer Netherlands. - 0792321928 - 9401706255 - 9789048142538 - 9789401706254 ; , s. 107-126
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Bokkapitel (refereegranskat)abstract
- In summer 1987 most of the multibody dynamics community met at the JPL, Pasadena, to discuss the needs and the open problems in multibody system simulation, especially for space applications. P. W. Likins stated in his survey [16]: “Computational questions focused initially on the selection of subroutines for numerical integration, matrix inversion, or eigensystem analysis,and lately have shifted to preprocessors and postprocessors for user convenience. More fundamental issues are raised by the potential of symbolic manipulation and parallel processing, both of which present the possibility of revolutionizing the field.” Concepts for symbolic implementation have been pursued at various places, e.g. [14, 21]. This paper presents results of our efforts to exploit the potential of parallel computer architectures for multibody simulation. It has its roots in an analysis of the status of knowledge at the time, the above statement was made.
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| 18. |
- Franke, Cornelia, et al.
(författare)
-
Collocation Methods for the Investigation of Periodic Motions of Constrained Multibody Systems
- 2001
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Ingår i: Multibody System Dynamics. - 1384-5640. ; 5:2, s. 133-158
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Tidskriftsartikel (refereegranskat)abstract
- The investigation of periodic motions of constrained multibody systems requires the numerical solution of differential-algebraic boundary value problems. After briefly surveying the basics of periodic motion analysis the paper presents an extension of projected collocation methods [6] to a special class of boundary Value problems for multibody system equations with position and velocity constraints. These methods can be applied for computing stable as well as unstable periodic motions. Furthermore they provide stability information, which can be used to detect bifurcations on periodic branches. The special class of equations stemming from contact problems like in railroad systems [22] can be handled as well. Numerical experiments with a wheelset model demonstrate the performance of the algorithms
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| 19. |
- Führer, Claus, et al.
(författare)
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A computer-oriented method for reducing linearized multibody equations by incorporating constraints
- 1984
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825. ; 46:2, s. 169-175
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Tidskriftsartikel (refereegranskat)abstract
- Consider a spatial multibody system with rigid and elastic bodies. The bodies are linked by rigid interconnections (e.g. revolute joints) causing constraints, as well as by flexible interconnections (e.g. springs) causing applied forces. Small motions of the system with respect to a given nominal configuration can be described by linearized dynamic equations and kinematic constraint equations. We present a computer-oriented procedure which allows to develop a minimum number of these equations. There are three problems. First: algorithmic selection of position coordinates; second: condensation of the dynamic equations; third: evaluation of the constraint forces. To demonstrate the procedure, a closed loop multibody system is used as an example.
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| 20. |
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