The tangent stiffness matrix for an absolute interface coordinates floating frame of reference formulation

Jurnan Paul Schilder*, Marcellinus Hermannus Maria Ellenbroek, Klaas Simon Dwarshuis, A. de Boer

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

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    Abstract

    In this work, a full and complete development of the tangent stiffness matrix is presented, suitable for the use in an absolute interface coordinates floating frame of reference formulation. For simulation of flexible multibody systems, the floating frame formulation is used for its advantage to describe local elastic deformation by means of a body’s linear finite element model. Consequently, the powerful Craig–Bampton method can be applied for model order reduction. By establishing a coordinate transformation from the absolute floating frame coordinates and local interface coordinates corresponding to the Craig–Bampton modes to absolute interface coordinates, it is possible to satisfy kinematic constraints without the use of Lagrange multipliers. In this way, the floating frame does not need to be located at an interface point and can be positioned close to the body’s center of mass, without requiring an interface point at the center of mass. This improves simulation accuracy. In this work, the expression for the new method’s tangent stiffness matrix is obtained by taking the variation of the equation of equilibrium. The global tangent stiffness matrix is expressed as a local tangent stiffness matrix, consisting of both material stiffness and geometric stiffness terms, transformed to the global frame by the rotation matrix of the floating frame. Simulations of static and dynamic validation problems are performed. These simulations show the importance of including the tangent stiffness matrix for both convergence and simulation efficiency.
    Original languageEnglish
    Pages (from-to)243-263
    Number of pages21
    JournalMultibody system dynamics
    Volume47
    Issue number3
    Early online date26 Jul 2019
    DOIs
    Publication statusPublished - 1 Nov 2019

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    Stiffness matrix
    Stiffness Matrix
    Tangent line
    Formulation
    Barycentre
    Simulation
    Stiffness
    Lagrange multipliers
    Flexible multibody Systems
    Rotation matrix
    Model Order Reduction
    Elastic deformation
    Elastic Deformation
    Coordinate Transformation
    Kinematics
    Finite Element Model
    Term

    Keywords

    • UT-Hybrid-D

    Cite this

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    title = "The tangent stiffness matrix for an absolute interface coordinates floating frame of reference formulation",
    abstract = "In this work, a full and complete development of the tangent stiffness matrix is presented, suitable for the use in an absolute interface coordinates floating frame of reference formulation. For simulation of flexible multibody systems, the floating frame formulation is used for its advantage to describe local elastic deformation by means of a body’s linear finite element model. Consequently, the powerful Craig–Bampton method can be applied for model order reduction. By establishing a coordinate transformation from the absolute floating frame coordinates and local interface coordinates corresponding to the Craig–Bampton modes to absolute interface coordinates, it is possible to satisfy kinematic constraints without the use of Lagrange multipliers. In this way, the floating frame does not need to be located at an interface point and can be positioned close to the body’s center of mass, without requiring an interface point at the center of mass. This improves simulation accuracy. In this work, the expression for the new method’s tangent stiffness matrix is obtained by taking the variation of the equation of equilibrium. The global tangent stiffness matrix is expressed as a local tangent stiffness matrix, consisting of both material stiffness and geometric stiffness terms, transformed to the global frame by the rotation matrix of the floating frame. Simulations of static and dynamic validation problems are performed. These simulations show the importance of including the tangent stiffness matrix for both convergence and simulation efficiency.",
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    The tangent stiffness matrix for an absolute interface coordinates floating frame of reference formulation. / Schilder, Jurnan Paul; Ellenbroek, Marcellinus Hermannus Maria; Dwarshuis, Klaas Simon; de Boer, A.

    In: Multibody system dynamics, Vol. 47, No. 3, 01.11.2019, p. 243-263.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - Ellenbroek, Marcellinus Hermannus Maria

    AU - Dwarshuis, Klaas Simon

    AU - de Boer, A.

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