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A virtual element method for transversely isotropic elasticity

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Abstract

This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order virtual element method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored. In the latter case various options are considered for approximating the non-homogeneous fibre directions at an element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to both mild and strong non-homogeneity. Further, the convergence rate of the VEM is shown to be comparable to classical low-order standard finite element approaches.

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Acknowledgements

This work was carried out with support from the National Research Foundation of South Africa, through the South African Research Chair in Computational Mechanics. The authors acknowledge with thanks this support.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics and Centre for Research in Computational and Applied Mechanics, University of Cape Town, Rondebosch, 7701, South Africa

    B. D. Reddy

  2. Department of Mechanical Engineering and Centre for Research in Computational and Applied Mechanics, University of Cape Town, Rondebosch, 7701, South Africa

    D. van Huyssteen

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  1. B. D. Reddy
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  2. D. van Huyssteen
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Correspondence to D. van Huyssteen.

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Reddy, B.D., van Huyssteen, D. A virtual element method for transversely isotropic elasticity. Comput Mech 64, 971–988 (2019). https://doi.org/10.1007/s00466-019-01690-7

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