Numerical methods for simulation in applied dynamics

Applied dynamics may be considered as integration platform for simulation in various fields of engineering like vehicle system dynamics, dynamics of machines and mechanisms and robotics. In the present contribution we discuss classical numerical simulation techniques of nonlinear system dynamics, their use in multibody system simulation and extensions to typical problems of applied dynamics like continuous and discrete controllers and multidisciplinary applications. A frequently used alternative approach to the analysis of multidisciplinary problems is based on the coupling of two or more monodisciplinary simulation packages. Typical numerical problems of such co-simulation techniques will be considered and illustrated by numerical tests.

[1]  Martin Arnold,et al.  Wear profiles and the dynamical simulation of wheel-rail systems , 1997 .

[2]  Martin Arnold,et al.  Multi-Rate Time Integration for Large Scale Multibody System Models , 2007 .

[3]  Andreas Pfeiffer Numerische Sensitivitätsanalyse unstetiger multidisziplinärer Modelle mit Anwendungen in der gradientenbasierten Optimierung , 2008 .

[4]  Martin Otter,et al.  A very efficient algorithm for the simulation of robots and similar multibody systems without invers , 1986 .

[5]  Martin Spieck,et al.  Aeroelastic Effects in Multibody Dynamics , 2004 .

[6]  Martin Arnold,et al.  EFFICIENT SIMULATION OF BUSH AND ROLLER CHAIN DRIVES , 2005 .

[7]  S. Dietz,et al.  Vibration and Fatigue Analysis of Vehicle Systems Using Component Modes , 1999 .

[8]  Peter Lugner,et al.  Systemdynamik und Regelung von Fahrzeugen , 1994 .

[9]  Kenneth R. Jackson,et al.  A survey of parallel numerical methods for initial value problems for ordinary differential equations , 1991 .

[10]  Ondrej Vaculin,et al.  Multibody formalism for real-time application using natural coordinates and modified state space , 2007 .

[11]  K. Johnson,et al.  Three-Dimensional Elastic Bodies in Rolling Contact , 1990 .

[12]  Gregory M. Hulbert,et al.  A Gluing Algorithm for Network-Distributed Multibody Dynamics Simulation , 2001 .

[13]  M. Arnold,et al.  Index Reduction und Linearization in Industrial Multibody System Simulation , 2001 .

[14]  Friedrich Pfeiffer,et al.  Multibody Dynamics with Unilateral Contacts , 1996 .

[15]  Olivier Bruls,et al.  Modelling, simulation and control of flexible multibody systems , 2008 .

[16]  R. Schwertassek,et al.  Dynamik flexibler Mehrkörpersysteme , 1999 .

[17]  Michael Günther,et al.  Preconditioned Dynamic Iteration for Coupled Differential-Algebraic Systems , 2001 .

[18]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[19]  Michael Valášek,et al.  Methodologies for Coupling Simulation Models and Codes in Mechatronic System Analysis and Design , 2021, The Dynamics of Vehicles on Roads and on Tracks.

[20]  L. Petzold Differential/Algebraic Equations are not ODE's , 1982 .

[21]  Hans B. Pacejka,et al.  Tyre Models for Vehicle Dynamics Analysis , 1995 .

[22]  M. Arnold A perturbation analysis for the dynamical simulation of mechanical multibody systems , 1995 .

[23]  E. Eich Convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints , 1993 .

[24]  Pieter C. Breedveld Port-based modelling of multidomain physical systems in terms of bond graphs , 2008 .

[25]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[26]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[27]  Michael Tiller,et al.  Introduction to Physical Modeling with Modelica , 2001 .

[28]  Hans B. Pacejka,et al.  Recent advances in tyre models and testing procedures , 2005 .

[29]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[30]  B. Leimkuhler,et al.  Numerical solution of differential-algebraic equations for constrained mechanical motion , 1991 .

[31]  Wayne R. Cowell,et al.  Sources and development of mathematical software , 1984 .

[32]  Martin Arnold,et al.  Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs , 2007 .

[33]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[34]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[35]  Reinhold von Schwerin MultiBody System SIMulation - Numerical Methods, Algorithms, and Software , 1999, Lecture Notes in Computational Science and Engineering.

[36]  Cleve B. Moler,et al.  Numerical computing with MATLAB , 2004 .

[37]  C. W. Gear,et al.  Automatic integration of Euler-Lagrange equations with constraints , 1985 .

[38]  Werner Schiehlen,et al.  Software Tools: From Multibody System Analysis to Vehicle System Dynamics , 2001 .

[39]  U. Nowak,et al.  Numerical Integration of Constrained Mechanical Systems Using MEXX , 1995 .

[40]  Simon Iwnicki,et al.  The Manchester Benchmarks for Rail Vehicle Simulation , 1998 .

[41]  Per Lötstedt,et al.  Numerical solution of nonlinear differential equations with algebraic contraints II: practical implications , 1986 .

[42]  M. Arnold Numerical problems in the dynamical simulation of wheel-rail systems , 1996 .

[43]  Delf Sachau,et al.  Fatigue Life Predictions by Coupling Finite Element and Multibody Systems Calculations. , 1997 .

[44]  Stig Skelboe Stability properties of backward euler multirate formulas , 1989 .

[45]  E. Hairer,et al.  Stiff and differential-algebraic problems , 1991 .

[46]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[47]  Michael Valášek,et al.  Overview of Coupling of Multibody and Control Engineering Tools , 2004 .

[48]  Martin Busch Entwicklung einer SIMPACK-Modelica/Dymola Schnittstelle , 2007 .

[49]  Volker Mehrmann,et al.  A New Software Package for Linear Differential-Algebraic Equations , 1997, SIAM J. Sci. Comput..

[50]  Werner Schiehlen,et al.  Two Methods of Simulator Coupling , 2000 .

[51]  Thomas F. Coleman,et al.  Software for estimating sparse Jacobian matrices , 1984, ACM Trans. Math. Softw..

[52]  W. Rulka Effiziente Simulation der Dynamik mechatronischer Systeme für industrielle Anwendungen , 2001 .

[53]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[54]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[55]  J. Baumgarte Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[56]  Martin P. Bendsøe,et al.  Progress in Industrial Mathematics at ECMI 96 , 1997 .

[57]  Manfred Plöchl,et al.  Tyre model performance test: First experiences and results , 2005 .

[58]  Werner Schiehlen,et al.  General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms , 1985 .

[59]  Michael Valášek,et al.  Modeling, simulation and control of mechatronical systems , 2008 .

[60]  U. Ascher,et al.  Stabilization of DAEs and invariant manifolds , 1994 .

[61]  O. Wallrapp Linearized Flexible Multibody Dynamics Including Geometric Stiffening Effects , 1991 .

[62]  P. Deuflhard,et al.  One-step and extrapolation methods for differential-algebraic systems , 1987 .

[63]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[64]  Peter Eberhard,et al.  Multibody Systems and Applied Dynamics , 2008 .

[65]  Oskar Wallrapp,et al.  Standardization of flexible body modeling in multibody system codes , 1994 .

[66]  P. Rentrop,et al.  Differential-algebraic Equations in Vehicle System Dynamics , 1991 .

[67]  C. Kelley Solving Nonlinear Equations with Newton's Method , 1987 .

[68]  Martin Arnold,et al.  A Modal Multifield Approach for an Extended Flexible Body Description in Multibody Dynamics , 2005 .

[69]  C. W. Gear,et al.  Multirate linear multistep methods , 1984 .

[70]  E. Fuehrer C. Eich,et al.  Numerical Methods in Multibody Dynamies , 1992 .

[71]  Martin Otter,et al.  Inline Integration: A New Mixed Symbolic/Numeric Approach for Solving Differential-Algebraic Equations Systems , 1995 .

[72]  Martin Arnold,et al.  Efficient corrector iteration for DAE time integration in multibody dynamics , 2006 .

[73]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .