A Virtual Element Method for transversely isotropic elasticity
Numerical Analysis
2019-03-06 v3 Analysis of PDEs
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.
Cite
@article{arxiv.1810.00688,
title = {A Virtual Element Method for transversely isotropic elasticity},
author = {D. van Huyssteen and B. D. Reddy},
journal= {arXiv preprint arXiv:1810.00688},
year = {2019}
}