Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

  • Peter Betsch

Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 565)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Martin Arnold, Alberto Cardona, Olivier Brüls
    Pages 91-158
  3. Johannes Gerstmayr, Alexander Humer, Peter Gruber, Karin Nachbagauer
    Pages 159-200
  4. Adrián J. Lew, Pablo Mata A
    Pages 201-291

About this book


This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application of structure-preserving methods is illustrated by a number of examples dealing with, among others, nonlinear beams and shells, large deformation problems, long-term simulations and coupled thermo-mechanical multibody systems. In addition it links novel time integration methods to frequently used methods in industrial multibody system simulation.


Absolute Nodel Coordinate Formulation Energy-decaying Methods Energy-momentum Method Generalized-alpha Method Geometrically Exact Structural Models Lie-group Integrators Numerical Methods for Flexible multibody Dynamics Structure-preserving Time Integration Variational Integrators

Editors and affiliations

  • Peter Betsch
    • 1
  1. 1.Institute of MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany

Bibliographic information

  • DOI
  • Copyright Information CISM International Centre for Mechanical Sciences 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-31877-6
  • Online ISBN 978-3-319-31879-0
  • Series Print ISSN 0254-1971
  • Series Online ISSN 2309-3706
  • Buy this book on publisher's site