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    Implementation of Rayleigh Damping for Local Nonlinear Dynamic Analysis Based on a Matrix Perturbation Approach

    Source: Journal of Structural Engineering:;2021:;Volume ( 147 ):;issue: 009::page 04021130-1
    Author:
    Ding-Hao Yu
    ,
    Gang Li
    ,
    Hong-Nan Li
    DOI: 10.1061/(ASCE)ST.1943-541X.0003105
    Publisher: ASCE
    Abstract: Nonlinear analyses of structures under dynamic excitation are becoming increasingly important in structural design and performance evaluation, but large computational effort is the main factor that limits their application. Because nonlinearity is commonly confined within small regions, many studies have been devoted to improving the efficiency of solving such local nonlinear problems by maintaining the structural stiffness elasticity and simulating the effects of local nonlinearity through fictitious nonlinear forces or local modification of the elastic structural response. For dynamic analysis, the nature of the stiffness matrix determines the formulation of the widely used Rayleigh damping; as a result, these local nonlinear analysis methods often use elastic stiffness-based Rayleigh damping models. However, such a damping model can generate unexpected artificial damping forces for inelastic systems and consequently produce inaccurate or even invalid results. Although a tangent stiffness–based Rayleigh damping model has been proven to be a reasonable basis for performing highly accurate dynamic analyses, this type of damping model has difficulty achieving direct compatibility with local nonlinear analysis methods. The present research focuses on the implementation of a tangent stiffness–based Rayleigh damping model for use in efficient local nonlinear analysis methods developed based on the Woodbury formula, which can calculate the structural inelastic behavior by updating the elastic solution rather than by updating the stiffness. By representing tangent stiffness–based Rayleigh damping as a low-rank perturbation to the elastic stiffness-based damping matrix, this study derives a modified dynamic Woodbury formula in which an additional influence coefficient is introduced to reflect the effects of local nonlinearity on the structural damping properties. Moreover, to overcome the potential solution difficulty caused by abrupt changes in the damping forces in certain steps and further improve the efficiency of the proposed method, a variable time step solution scheme that can meet the computational requirements of the Woodbury formula is presented. Verifications demonstrate the validity and high efficiency of the proposed method.
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      Implementation of Rayleigh Damping for Local Nonlinear Dynamic Analysis Based on a Matrix Perturbation Approach

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4272750
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    • Journal of Structural Engineering

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    contributor authorDing-Hao Yu
    contributor authorGang Li
    contributor authorHong-Nan Li
    date accessioned2022-02-01T22:10:03Z
    date available2022-02-01T22:10:03Z
    date issued9/1/2021
    identifier other%28ASCE%29ST.1943-541X.0003105.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4272750
    description abstractNonlinear analyses of structures under dynamic excitation are becoming increasingly important in structural design and performance evaluation, but large computational effort is the main factor that limits their application. Because nonlinearity is commonly confined within small regions, many studies have been devoted to improving the efficiency of solving such local nonlinear problems by maintaining the structural stiffness elasticity and simulating the effects of local nonlinearity through fictitious nonlinear forces or local modification of the elastic structural response. For dynamic analysis, the nature of the stiffness matrix determines the formulation of the widely used Rayleigh damping; as a result, these local nonlinear analysis methods often use elastic stiffness-based Rayleigh damping models. However, such a damping model can generate unexpected artificial damping forces for inelastic systems and consequently produce inaccurate or even invalid results. Although a tangent stiffness–based Rayleigh damping model has been proven to be a reasonable basis for performing highly accurate dynamic analyses, this type of damping model has difficulty achieving direct compatibility with local nonlinear analysis methods. The present research focuses on the implementation of a tangent stiffness–based Rayleigh damping model for use in efficient local nonlinear analysis methods developed based on the Woodbury formula, which can calculate the structural inelastic behavior by updating the elastic solution rather than by updating the stiffness. By representing tangent stiffness–based Rayleigh damping as a low-rank perturbation to the elastic stiffness-based damping matrix, this study derives a modified dynamic Woodbury formula in which an additional influence coefficient is introduced to reflect the effects of local nonlinearity on the structural damping properties. Moreover, to overcome the potential solution difficulty caused by abrupt changes in the damping forces in certain steps and further improve the efficiency of the proposed method, a variable time step solution scheme that can meet the computational requirements of the Woodbury formula is presented. Verifications demonstrate the validity and high efficiency of the proposed method.
    publisherASCE
    titleImplementation of Rayleigh Damping for Local Nonlinear Dynamic Analysis Based on a Matrix Perturbation Approach
    typeJournal Paper
    journal volume147
    journal issue9
    journal titleJournal of Structural Engineering
    identifier doi10.1061/(ASCE)ST.1943-541X.0003105
    journal fristpage04021130-1
    journal lastpage04021130-13
    page13
    treeJournal of Structural Engineering:;2021:;Volume ( 147 ):;issue: 009
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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