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    On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics

    Source: Journal of Applied Mechanics:;1975:;volume( 042 ):;issue: 004::page 865
    Author:
    T. Belytschko
    ,
    D. F. Schoeberle
    DOI: 10.1115/1.3423721
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: In this paper an implicit Newmark β-method with iterations for nonlinear structural dynamics is described; the algorithm is identical to standard algorithms except that a new convergence criterion is employed. A discrete energy is defined and it is shown that this discrete energy is bounded regardless of the size of the time step; this is a sufficient condition for the unconditional stability of the algorithm for nonlinear material problems. Numerical examples are given for problems with both geometric and material nonlinearities.
    keyword(s): Stability , Structural dynamics AND Algorithms ,
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      On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics

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    http://yetl.yabesh.ir/yetl1/handle/yetl/86986
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    contributor authorT. Belytschko
    contributor authorD. F. Schoeberle
    date accessioned2017-05-08T22:57:39Z
    date available2017-05-08T22:57:39Z
    date copyrightDecember, 1975
    date issued1975
    identifier issn0021-8936
    identifier otherJAMCAV-26047#865_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/86986
    description abstractIn this paper an implicit Newmark β-method with iterations for nonlinear structural dynamics is described; the algorithm is identical to standard algorithms except that a new convergence criterion is employed. A discrete energy is defined and it is shown that this discrete energy is bounded regardless of the size of the time step; this is a sufficient condition for the unconditional stability of the algorithm for nonlinear material problems. Numerical examples are given for problems with both geometric and material nonlinearities.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics
    typeJournal Paper
    journal volume42
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3423721
    journal fristpage865
    journal lastpage869
    identifier eissn1528-9036
    keywordsStability
    keywordsStructural dynamics AND Algorithms
    treeJournal of Applied Mechanics:;1975:;volume( 042 ):;issue: 004
    contenttypeFulltext
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