Quantitative Study of the Stabilization Parameter in the Virtual Element Method

Russo, Alessandro; Sukumar, N.

doi:10.1007/978-3-031-53740-0_14

CIM Series in Mathematical Sciences

2024

DOI: 10.1007/978-3-031-53740-0_14

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Quantitative Study of the Stabilization Parameter in the Virtual Element Method

Alessandro Russo,

N. Sukumar

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2024

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Axisymmetric virtual elements for problems of elasticity and plasticity

Yaw

2024

Numerical Meth Engineering

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The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

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Axisymmetric virtual elements for problems of elasticity and plasticity

Yaw

2024

Numerical Meth Engineering

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Quantitative Study of the Stabilization Parameter in the Virtual Element Method

Cited by 1 publication

References 11 publications

Axisymmetric virtual elements for problems of elasticity and plasticity

Axisymmetric virtual elements for problems of elasticity and plasticity

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