Importance of Warping in Beams with Narrow Rectangular Cross-Sections: An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study

Marijn Nijenhuis*, Ben Jonker, Dannis Brouwer

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    Abstract

    This paper reports on the significance of warping deformation on the stability analysis of a flexible cross-hinge mechanism, which consists of two leaf springs with rectangular cross-section. The effect of misalignments in this mechanism is studied analytically, numerically and experimentally. An analytical buckling analysis is carried out to determine the theoretical critical load of a generalized cross-hinge mechanism on the basis of first principles. A geometrically nonlinear beam finite element with a non-uniform torsion description is used to model the leaf springs numerically. The change in natural mode frequencies and stiffness as a function of the misalignment is determined by a multibody program. Measurements from a dedicated experimental set-up confirm that the inclusion of warping effects is crucial, even for narrow rectangular cross-sections: it is found that the effects of warping increase the analytical critical buckling load of the system by 55%.

    Original languageEnglish
    Title of host publicationMultibody Dynamics 2019
    Subtitle of host publicationProceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics
    EditorsAndrés Kecskeméthy, Francisco Geu Flores
    Place of PublicationCham
    PublisherSpringer
    Pages199-206
    Number of pages8
    ISBN (Electronic)978-3-030-23132-3
    ISBN (Print)978-3-030-23131-6
    DOIs
    Publication statusPublished - 1 Jan 2020
    EventMultibody Dynamics 2019: 9th ECCOMAS Thematic Conference - University of Duisburg-Essen, Duisburg, Germany
    Duration: 15 Jul 201918 Jul 2019

    Publication series

    NameComputational Methods in Applied Sciences
    PublisherSpringer
    Volume53
    ISSN (Print)1871-3033

    Conference

    ConferenceMultibody Dynamics 2019
    CountryGermany
    CityDuisburg
    Period15/07/1918/07/19

    Fingerprint

    Leaf springs
    Warping
    Hinges
    Buckling
    Cross section
    Misalignment
    Leaves
    Torsional stress
    Critical Load
    Stiffness
    First-principles
    Torsion
    Stability Analysis
    Inclusion
    Finite Element
    Model

    Cite this

    Nijenhuis, M., Jonker, B., & Brouwer, D. (2020). Importance of Warping in Beams with Narrow Rectangular Cross-Sections: An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study. In A. Kecskeméthy, & F. Geu Flores (Eds.), Multibody Dynamics 2019: Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics (pp. 199-206). (Computational Methods in Applied Sciences; Vol. 53). Cham: Springer. https://doi.org/10.1007/978-3-030-23132-3_24
    Nijenhuis, Marijn ; Jonker, Ben ; Brouwer, Dannis. / Importance of Warping in Beams with Narrow Rectangular Cross-Sections : An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study. Multibody Dynamics 2019: Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics. editor / Andrés Kecskeméthy ; Francisco Geu Flores. Cham : Springer, 2020. pp. 199-206 (Computational Methods in Applied Sciences).
    @inbook{ccf779abefc44edebceaa1fc0e86b12b,
    title = "Importance of Warping in Beams with Narrow Rectangular Cross-Sections: An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study",
    abstract = "This paper reports on the significance of warping deformation on the stability analysis of a flexible cross-hinge mechanism, which consists of two leaf springs with rectangular cross-section. The effect of misalignments in this mechanism is studied analytically, numerically and experimentally. An analytical buckling analysis is carried out to determine the theoretical critical load of a generalized cross-hinge mechanism on the basis of first principles. A geometrically nonlinear beam finite element with a non-uniform torsion description is used to model the leaf springs numerically. The change in natural mode frequencies and stiffness as a function of the misalignment is determined by a multibody program. Measurements from a dedicated experimental set-up confirm that the inclusion of warping effects is crucial, even for narrow rectangular cross-sections: it is found that the effects of warping increase the analytical critical buckling load of the system by 55{\%}.",
    author = "Marijn Nijenhuis and Ben Jonker and Dannis Brouwer",
    year = "2020",
    month = "1",
    day = "1",
    doi = "10.1007/978-3-030-23132-3_24",
    language = "English",
    isbn = "978-3-030-23131-6",
    series = "Computational Methods in Applied Sciences",
    publisher = "Springer",
    pages = "199--206",
    editor = "Andr{\'e}s Kecskem{\'e}thy and {Geu Flores}, Francisco",
    booktitle = "Multibody Dynamics 2019",

    }

    Nijenhuis, M, Jonker, B & Brouwer, D 2020, Importance of Warping in Beams with Narrow Rectangular Cross-Sections: An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study. in A Kecskeméthy & F Geu Flores (eds), Multibody Dynamics 2019: Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics. Computational Methods in Applied Sciences, vol. 53, Springer, Cham, pp. 199-206, Multibody Dynamics 2019, Duisburg, Germany, 15/07/19. https://doi.org/10.1007/978-3-030-23132-3_24

    Importance of Warping in Beams with Narrow Rectangular Cross-Sections : An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study. / Nijenhuis, Marijn; Jonker, Ben; Brouwer, Dannis.

    Multibody Dynamics 2019: Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics. ed. / Andrés Kecskeméthy; Francisco Geu Flores. Cham : Springer, 2020. p. 199-206 (Computational Methods in Applied Sciences; Vol. 53).

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    TY - CHAP

    T1 - Importance of Warping in Beams with Narrow Rectangular Cross-Sections

    T2 - An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study

    AU - Nijenhuis, Marijn

    AU - Jonker, Ben

    AU - Brouwer, Dannis

    PY - 2020/1/1

    Y1 - 2020/1/1

    N2 - This paper reports on the significance of warping deformation on the stability analysis of a flexible cross-hinge mechanism, which consists of two leaf springs with rectangular cross-section. The effect of misalignments in this mechanism is studied analytically, numerically and experimentally. An analytical buckling analysis is carried out to determine the theoretical critical load of a generalized cross-hinge mechanism on the basis of first principles. A geometrically nonlinear beam finite element with a non-uniform torsion description is used to model the leaf springs numerically. The change in natural mode frequencies and stiffness as a function of the misalignment is determined by a multibody program. Measurements from a dedicated experimental set-up confirm that the inclusion of warping effects is crucial, even for narrow rectangular cross-sections: it is found that the effects of warping increase the analytical critical buckling load of the system by 55%.

    AB - This paper reports on the significance of warping deformation on the stability analysis of a flexible cross-hinge mechanism, which consists of two leaf springs with rectangular cross-section. The effect of misalignments in this mechanism is studied analytically, numerically and experimentally. An analytical buckling analysis is carried out to determine the theoretical critical load of a generalized cross-hinge mechanism on the basis of first principles. A geometrically nonlinear beam finite element with a non-uniform torsion description is used to model the leaf springs numerically. The change in natural mode frequencies and stiffness as a function of the misalignment is determined by a multibody program. Measurements from a dedicated experimental set-up confirm that the inclusion of warping effects is crucial, even for narrow rectangular cross-sections: it is found that the effects of warping increase the analytical critical buckling load of the system by 55%.

    UR - http://www.scopus.com/inward/record.url?scp=85068188198&partnerID=8YFLogxK

    U2 - 10.1007/978-3-030-23132-3_24

    DO - 10.1007/978-3-030-23132-3_24

    M3 - Chapter

    AN - SCOPUS:85068188198

    SN - 978-3-030-23131-6

    T3 - Computational Methods in Applied Sciences

    SP - 199

    EP - 206

    BT - Multibody Dynamics 2019

    A2 - Kecskeméthy, Andrés

    A2 - Geu Flores, Francisco

    PB - Springer

    CY - Cham

    ER -

    Nijenhuis M, Jonker B, Brouwer D. Importance of Warping in Beams with Narrow Rectangular Cross-Sections: An Analytical, Numerical and Experimental Flexible Cross-Hinge Case Study. In Kecskeméthy A, Geu Flores F, editors, Multibody Dynamics 2019: Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics. Cham: Springer. 2020. p. 199-206. (Computational Methods in Applied Sciences). https://doi.org/10.1007/978-3-030-23132-3_24