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Numerical methods in vehicle system dynamics: state of the art and current developments

Arnold, Martin; Burgermeister, Bernhard; Führer, Claus LU ; Hippmann, Gerhard and Rill, Georg (2011) In Vehicle System Dynamics 49(7). p.1159-1207
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
vehicle system dynamics, differential-algebraic equations, differential equations, numerical methods
in
Vehicle System Dynamics
volume
49
issue
7
pages
1159 - 1207
publisher
Taylor & Francis
external identifiers
  • wos:000298956300006
  • scopus:84856867049
ISSN
1744-5159
DOI
10.1080/00423114.2011.582953
language
English
LU publication?
yes
id
d3d3f208-6eb3-4fa1-8d9b-b5aaad851ffa (old id 2163389)
alternative location
http://dx.doi.org/10.1080/00423114.2011.582953
date added to LUP
2011-10-19 13:03:19
date last changed
2017-09-03 03:20:54
@article{d3d3f208-6eb3-4fa1-8d9b-b5aaad851ffa,
  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.<br/><br>
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<br/><br>
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.<br/><br>
Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics.<br/><br>
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.<br/><br>
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<br/><br>
iii) Modelling and time integration of multidisciplinary problems in system dynamics including co-simulation techniques.},
  author       = {Arnold, Martin and Burgermeister, Bernhard and Führer, Claus and Hippmann, Gerhard and Rill, Georg},
  issn         = {1744-5159},
  keyword      = {vehicle system dynamics,differential-algebraic equations,differential equations,numerical methods},
  language     = {eng},
  number       = {7},
  pages        = {1159--1207},
  publisher    = {Taylor & Francis},
  series       = {Vehicle System Dynamics},
  title        = {Numerical methods in vehicle system dynamics: state of the art and current developments},
  url          = {http://dx.doi.org/10.1080/00423114.2011.582953},
  volume       = {49},
  year         = {2011},
}