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

Cremonesi, M;Perego, U;
2023-01-01

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.
2023
Linear elasticity
Hu-Washizu formulation
Virtual Element Method
Hourglass stabilization
Self-stabilized Virtual Elements
Locking-free
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1263931
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