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    Exact Sensitivity of Nonlinear Dynamic Response with Modal and Rayleigh Damping Formulated with the Tangent Stiffness

    Source: Journal of Structural Engineering:;2024:;Volume ( 150 ):;issue: 003::page 04024012-1
    Author:
    Terje Haukaas
    DOI: 10.1061/JSENDH.STENG-12604
    Publisher: ASCE
    Abstract: Derivatives of nonlinear dynamic response are calculated in an exact and efficient manner with respect to material, geometry, mass, and damping parameters. Developments are presented for the Rayleigh and modal damping options that use the updated tangent stiffness. The calculation of exact response sensitivities for those options requires the calculation of derivatives of eigenvalues and eigenvectors; it is also shown that the third-order tensor formed by the derivative of the stiffness matrix with respect to the displacement vector is needed. That tensor, which amends the coefficient matrix of the system of equations that governs the response sensitivities, is nonzero for materials with continuously varying stiffness. The Bouc–Wen material model exhibits that feature and is selected to demonstrate the developments. Correct differentiation and assembly at the material, section, and element levels are highlighted. The results, verified by finite difference, suggest that the sensitivity of the response is influenced by the choice of damping model, strongly for some parameters, particularly when higher modes contribute to the nonlinear structural behavior.
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      Exact Sensitivity of Nonlinear Dynamic Response with Modal and Rayleigh Damping Formulated with the Tangent Stiffness

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4296787
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    contributor authorTerje Haukaas
    date accessioned2024-04-27T22:29:44Z
    date available2024-04-27T22:29:44Z
    date issued2024/03/01
    identifier other10.1061-JSENDH.STENG-12604.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4296787
    description abstractDerivatives of nonlinear dynamic response are calculated in an exact and efficient manner with respect to material, geometry, mass, and damping parameters. Developments are presented for the Rayleigh and modal damping options that use the updated tangent stiffness. The calculation of exact response sensitivities for those options requires the calculation of derivatives of eigenvalues and eigenvectors; it is also shown that the third-order tensor formed by the derivative of the stiffness matrix with respect to the displacement vector is needed. That tensor, which amends the coefficient matrix of the system of equations that governs the response sensitivities, is nonzero for materials with continuously varying stiffness. The Bouc–Wen material model exhibits that feature and is selected to demonstrate the developments. Correct differentiation and assembly at the material, section, and element levels are highlighted. The results, verified by finite difference, suggest that the sensitivity of the response is influenced by the choice of damping model, strongly for some parameters, particularly when higher modes contribute to the nonlinear structural behavior.
    publisherASCE
    titleExact Sensitivity of Nonlinear Dynamic Response with Modal and Rayleigh Damping Formulated with the Tangent Stiffness
    typeJournal Article
    journal volume150
    journal issue3
    journal titleJournal of Structural Engineering
    identifier doi10.1061/JSENDH.STENG-12604
    journal fristpage04024012-1
    journal lastpage04024012-13
    page13
    treeJournal of Structural Engineering:;2024:;Volume ( 150 ):;issue: 003
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian