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Solution Methods for Nonlinear Evolution Problems

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Nonlinear Computational Structural Mechanics

Part of the book series: Mechanical Engineering Series ((MES))

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Abstract

Nearly all the methods one encounters in mechanics for solving nonlinear evolution problems are incremental methods. The load, or rather the interval of time [0, T] considered, is decomposed into a succession of (generally) small intervals. The history of different quantities being known until the present instant t, one studies a new interval of time [ t, t + Δt] where Δt is the increment. The problem is then to determine the history on the interval [t, t + Δt]. In assuming, for example, a linear history on [t, t + Δt] that is, a history that depends only on values at the instant t + Δt we are led to a classical nonlinear problem where the time does not enter. This problem, which determines various quantities at time t + Δt is generally treated by a Newton-type method. We note that the only mechanics property used is the principle of causality.

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© 1999 Springer Science+Business Media New York

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Ladevèze, P. (1999). Solution Methods for Nonlinear Evolution Problems. In: Nonlinear Computational Structural Mechanics. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1432-8_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1432-8_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7141-3

  • Online ISBN: 978-1-4612-1432-8

  • eBook Packages: Springer Book Archive

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