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

  • Book
  • © 2016

Overview

Editors:
  1. Peter Betsch

    1. Institute of Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  • Presents a state-of-the-art review of structure-preserving
  • numerical methods for constrained mechanical systems
  • Offers contemporary treatment of numerical methods for
  • flexible multibody dynamics
  • Outlines a comprehensive approach that yields an integrated simulation tool for flexible mechanism analysis
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. High Frequency Dissipative Integration Schemes for Linear and Nonlinear Elastodynamics

    • Ignacio Romero
    Pages 1-30

  3. Energy-Momentum Integrators for Elastic Cosserat Points, Rigid Bodies, and Multibody Systems

    • Peter Betsch
    Pages 31-89

  4. A Lie Algebra Approach to Lie Group Time Integration of Constrained Systems

    • Martin Arnold, Alberto Cardona, Olivier Brüls
    Pages 91-158

  5. The Absolute Nodal Coordinate Formulation

    • Johannes Gerstmayr, Alexander Humer, Peter Gruber, Karin Nachbagauer
    Pages 159-200

  6. A Brief Introduction to Variational Integrators

    • Adrián J. Lew, Pablo Mata A
    Pages 201-291
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Keywords

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.

Editors and Affiliations

  • Institute of Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Peter Betsch

Bibliographic Information

  • Book Title: Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

  • Editors: Peter Betsch

  • Series Title: CISM International Centre for Mechanical Sciences

  • DOI: https://doi.org/10.1007/978-3-319-31879-0

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: CISM International Centre for Mechanical Sciences 2016

  • Hardcover ISBN: 978-3-319-31877-6Published: 18 May 2016

  • Softcover ISBN: 978-3-319-81141-3Published: 27 May 2018

  • eBook ISBN: 978-3-319-31879-0Published: 10 May 2016

  • Series ISSN: 0254-1971

  • Series E-ISSN: 2309-3706

  • Edition Number: 1

  • Number of Pages: VII, 291

  • Number of Illustrations: 60 b/w illustrations, 20 illustrations in colour

  • Topics: Theoretical and Applied Mechanics, Applications of Nonlinear Dynamics and Chaos Theory

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