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On triangular virtual elements for Kirchhoff–Love shells.

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Title: On triangular virtual elements for Kirchhoff–Love shells.
Authors: Wu, T. P.1 (AUTHOR) tiagowu@usp.br, Pimenta, P. M.1 (AUTHOR), Wriggers, P.2 (AUTHOR)
Source: Archive of Applied Mechanics. Sep2024, Vol. 94 Issue 9, p2371-2404. 34p.
Subjects: Structural shells, Curvilinear coordinates, Polynomial approximation, Degrees of freedom, Elasticity
Abstract: We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works. [ABSTRACT FROM AUTHOR]
Copyright of Archive of Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Archive+of+Applied+Mechanics%22">Archive of Applied Mechanics</searchLink>. Sep2024, Vol. 94 Issue 9, p2371-2404. 34p.
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  Data: We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Archive of Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00419-024-02591-9
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        Text: English
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        Type: general
      – SubjectFull: Curvilinear coordinates
        Type: general
      – SubjectFull: Polynomial approximation
        Type: general
      – SubjectFull: Degrees of freedom
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      – SubjectFull: Elasticity
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              M: 09
              Text: Sep2024
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