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High Frequency Dissipative Integration Schemes for Linear and Nonlinear Elastodynamics

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

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

Abstract

Time integration schemes with controllable, artificial, high frequency dissipation are extremely common in practical engineering analyses for integrating in time initial boundary value problems previously discretized in space with finite elements or similar techniques. In this chapter, we describe the structure of the most commonly employed integration schemes of this type and focus in their numerical analysis for linear and nonlinear problems. These include spectral, energy, and backward error analyses. For the nonlinear case, additionally, we study the preservation of conservation laws and the approximation of relative equilibria. The chapter should provide a general overview of dissipative methods, their issues, and the tools available for their formulation and analysis.

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Acknowledgments

Funding for this work has been provided by the Spanish Ministry of Science and Competitiveness under Grant DPI2012-36429.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Technical University of Madrid, Madrid, Spain

    Ignacio Romero

  2. IMDEA Materials Institute, Getafe, Madrid, Spain

    Ignacio Romero

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  1. Ignacio Romero
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Correspondence to Ignacio Romero .

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Editors and Affiliations

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

    Peter Betsch

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Romero, I. (2016). High Frequency Dissipative Integration Schemes for Linear and Nonlinear Elastodynamics. In: Betsch, P. (eds) Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics. CISM International Centre for Mechanical Sciences, vol 565. Springer, Cham. https://doi.org/10.1007/978-3-319-31879-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-31879-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31877-6

  • Online ISBN: 978-3-319-31879-0

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