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Time-Stepping Algorithms in Nonlinear Resultant Shell Dynamics

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Encyclopedia of Continuum Mechanics

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Synonyms

Dynamics in low natural frequency range; Energy conserving algorithms in shell dynamics; Nonlinear dynamics of shells

Definition

Time-stepping algorithms serve as the tool of temporal approximation of evolution equations of dynamical systems. The algorithms are divided into one-step and multistep methods depending on the number of the required preceding time steps. If the sought variable appears as explicit or implicit, the scheme is classified as explicit or implicit, respectively.

Introduction

While formulating the numerical schemes the following three criteria must be taken into account: consistency (relation between the differential equation and its discrete formulation); stability (relation between the computed solution and the exact solution of the discretized equations); convergence (connects the computed solution to the exact solution of the differential equation). In nonlinear dynamics of structures, where the interest is focused on the range of low values of natural...

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Author information

Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Jacek Chróścielewski & Wojciech Witkowski

Authors
  1. Jacek Chróścielewski
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  2. Wojciech Witkowski
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Corresponding author

Correspondence to Jacek Chróścielewski .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Gdańsk, Poland

    Wojciech Pietraszkiewicz

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Chróścielewski, J., Witkowski, W. (2018). Time-Stepping Algorithms in Nonlinear Resultant Shell Dynamics. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_196-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_196-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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