3D stabilization-free virtual element method for linear elastic analysis

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OriginalspracheEnglisch
Aufsatznummer116826
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang421
Frühes Online-Datum2 Feb. 2024
PublikationsstatusVeröffentlicht - 1 März 2024

Abstract

We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.

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3D stabilization-free virtual element method for linear elastic analysis. / Xu, Bing Bing; Wriggers, Peter.
in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 421, 116826, 01.03.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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abstract = "We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.",
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AU - Xu, Bing Bing

AU - Wriggers, Peter

N1 - Funding Information: The authors are grateful for the support provided by the Alexander von Humboldt Foundation, Germany . The first author thanks Dr. Jian Meng and Professor Alessandro Russo for discussions on the enhancement space.

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N2 - We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.

AB - We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.

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