An original, variational formulation of the Virtual Element Method (VEM) is proposed, based on a Hu–Washizu mixed variational statement for 2D linear elastostatics. The proposed variational framework appears to be ideal for the formulation of VEs, whereby compatibility is enforced in a weak sense and the strain model can be prescribed a priori, independently of the unknown displacement model. It is shown how the ensuing freedom in the definition of the strain model can be conveniently exploited for the formulation of self-stabilized and possibly locking-free low order VEs. The superior performances of the VEs formulated within this framework has been verified by application to several numerical tests.

A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics / A. Lamperti, M. Cremonesi, U. Perego, A. Russo, C. Lovadina. - In: COMPUTATIONAL MECHANICS. - ISSN 0178-7675. - 71:5(2023 May), pp. 935-955. [10.1007/s00466-023-02282-2]

A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics

C. Lovadina
2023

Abstract

An original, variational formulation of the Virtual Element Method (VEM) is proposed, based on a Hu–Washizu mixed variational statement for 2D linear elastostatics. The proposed variational framework appears to be ideal for the formulation of VEs, whereby compatibility is enforced in a weak sense and the strain model can be prescribed a priori, independently of the unknown displacement model. It is shown how the ensuing freedom in the definition of the strain model can be conveniently exploited for the formulation of self-stabilized and possibly locking-free low order VEs. The superior performances of the VEs formulated within this framework has been verified by application to several numerical tests.
Hourglass stabilization; Hu–Washizu formulation; Linear elasticity; Locking-free; Self-stabilized Virtual Elements; Virtual Element Method;
Settore ICAR/08 - Scienza delle Costruzioni
mag-2023
28-feb-2023
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1001810
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