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On triangular virtual elements for Kirchhoff–Love shells

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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.

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Data Availability Statement

No datasets were generated or analysed during the current study.

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Acknowledgements

T.P. Wu acknowledges the support by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)-Finance Code 001. P.M. Pimenta gratefully acknowledges the support by ANR-FAPESP through the thematic grant 2020/13362-1 with the title “Mechanics, Stochastics and Control with Code-Coupling: System-of-Multibody-Systems point-of-view to Optimize Off-Shore/In-Land Farms of Wind Turbines with Flexible Blades” that made this work possible. P.M. Pimenta also acknowledges the support by CNPq under the Grant 308142/2018-7 and by the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stays at the Universities of Duisburg-Essen and Hannover in Germany.

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Author notes

  1. P. M. Pimenta and P. Wriggers have contributed equally to this work.

Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, University of São Paulo, Av. Prof. Almeida Prado, 83, São Paulo, São Paulo, 05508-070, Brazil

    T. P. Wu & P. M. Pimenta

  2. Institute for Continuum Mechanics, Leibniz Universität Hannover, An der Universität 1, 30823, Hannover, Lower Saxony, Germany

    P. Wriggers

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  1. T. P. Wu
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P. M. Pimenta and P. Wriggers contributed equally to this work.

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Correspondence to T. P. Wu.

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Wu, T.P., Pimenta, P.M. & Wriggers, P. On triangular virtual elements for Kirchhoff–Love shells. Arch Appl Mech (2024). https://doi.org/10.1007/s00419-024-02591-9

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