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arXiv · 1810.00688

A Virtual Element Method for transversely isotropic elasticity

D. van Huyssteen·B. D. Reddy
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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 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 mild and strong non-homogeneity.

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D. van Huyssteen, B. D. Reddy. 2018-10-01. A Virtual Element Method for transversely isotropic elasticity. https://doi.org/10.1007/s00466-019-01690-7

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