The present work deals with the formulation of a virtual element method for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II (Artioli et al. in Comput Mech, 2017) the method is extended to material nonlinearity, considering different inelastic responses of the material. In particular, in part I a standardized procedure for the construction of all the terms required for the implementation of the method in a computer code is explained. The procedure is initially illustrated for the simplest case of quadrilateral virtual elements with linear approximation of displacement variables on the boundary of the element. Then, the case of polygonal elements with quadratic and, even, higher order interpolation is considered. The construction of the method is detailed, deriving the approximation of the consistent term, the required stabilization term and the loading term for all the considered virtual elements. A wide numerical investigation is performed to assess the performances of the developed virtual elements, considering different number of edges describing the elements and different order of approximations of the unknown field. Numerical results are also compared with the one recovered using the classical finite element method.

Artioli, E., BEIRAO DA VEIGA, L., Lovadina, C., Sacco, E. (2017). Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem. COMPUTATIONAL MECHANICS, 60(3), 355-377 [10.1007/s00466-017-1404-5].

Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem

BEIRAO DA VEIGA, LOURENCO;
2017

Abstract

The present work deals with the formulation of a virtual element method for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II (Artioli et al. in Comput Mech, 2017) the method is extended to material nonlinearity, considering different inelastic responses of the material. In particular, in part I a standardized procedure for the construction of all the terms required for the implementation of the method in a computer code is explained. The procedure is initially illustrated for the simplest case of quadrilateral virtual elements with linear approximation of displacement variables on the boundary of the element. Then, the case of polygonal elements with quadratic and, even, higher order interpolation is considered. The construction of the method is detailed, deriving the approximation of the consistent term, the required stabilization term and the loading term for all the considered virtual elements. A wide numerical investigation is performed to assess the performances of the developed virtual elements, considering different number of edges describing the elements and different order of approximations of the unknown field. Numerical results are also compared with the one recovered using the classical finite element method.
Articolo in rivista - Articolo scientifico
Elasticity; Polygonal meshes; Static analysis; Virtual element method;
Elasticity; Polygonal meshes; Static analysis; Virtual element method; Ocean Engineering; Mechanical Engineering; Computational Theory and Mathematics; Computational Mathematics; Applied Mathematics
English
2017
60
3
355
377
none
Artioli, E., BEIRAO DA VEIGA, L., Lovadina, C., Sacco, E. (2017). Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem. COMPUTATIONAL MECHANICS, 60(3), 355-377 [10.1007/s00466-017-1404-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/178190
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