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Click on title above or here to access this collection. In this paper we propose and analyze a novel stream formulation of the virtual element method VEM for the solution of the Stokes problem. The new formulation hinges upon the introduction of a suitable stream function space characterizing the divergence free subspace of discrete velocities and it is equivalent to the velocity-pressure inf-sup stable mimetic scheme presented in [L.
Both schemes are thus stable and linearly convergent but the new method results to be more desirable as it employs much less degrees of freedom and it is based on a positive definite algebraic problem. Several numerical experiments assess the convergence properties of the new method and show its computational advantages with respect to the mimetic one.
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Publication Data. Publisher: Society for Industrial and Applied Mathematics. AntoniettiL. Moraand M. Cited by A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem.
Computer Methods in Applied Mechanics and Engineering International Journal for Numerical Methods in Engineering Advances in Computational Mathematics 46 Journal of Scientific Computing 85 Applied Numerical Mathematics Journal of Physics: Conference Series Journal of Scientific Computing 84 Mathematical Models and Methods in Applied Sciences 30 Mathematics and Computers in Simulation Journal of Scientific Computing 83 Mathematics in Computer Science Computer Aided Geometric Design 77 Mathematics in Engineering 2 :2, Akash AnandJeffrey S.
OvallSamuel E.In this paper, we employ the virtual element method for the numerical solution of linear thermo-elastic problems in two dimensions. The framework is implemented within the commercial software Abaqus using its user element feature. The implementation details of the virtual element method in Abaqus-Matlab software framework are described.
The corresponding details on the input data format, which forms the core of the analysis, are given. Both linear and quadratic elements are used within the virtual element framework. A few benchmark problems from linear thermo-elasticity are solved to validate the implementation.
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Talischi, C. Rand, A. Sze, K. Botsch, M. Jayabal, K. Jaskowiec, J. Biabanaki, S. Kravtsov, D. Pereira, A. Google Scholar. Lipnikov, K. Methods Appl. Models Methods Appl. Gain, A. Da Veiga, L. B 39 2 Droniou, J.This paper aims to propose a boundary element analysis of two-dimensional linear elasticity problems by a new expanding element interpolation method.
The expanding element is made up based on a traditional discontinuous element by adding virtual nodes along the perimeter of the element. The internal nodes of the original discontinuous element are referred to as source nodes and its shape function as raw shape function.
The shape functions of the expanding element constructed on both source nodes and virtual nodes are referred as fine shape functions. Boundary variables are interpolated by the fine shape functions, while the boundary integral equations are collocated on source nodes. The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages. The polynomial order of fine shape functions of the expanding elements increases by two compared with their corresponding raw shape functions, while the expanding elements still keep independence to each other as the original discontinuous elements.
This feature makes the expanding elements able to naturally and accurately interpolate both continuous and discontinuous fields. Numerical examples are presented to verify the proposed method.
SIAM Journal on Numerical Analysis
Results have demonstrated that the accuracy, efficiency and convergence rate of the expanding element method. Zhang, J. Report bugs here. Please share your general feedback. You can join in the discussion by joining the community or logging in here. You can also find out more about Emerald Engage.
Visit emeraldpublishing. Answers to the most commonly asked questions here. Abstract Purpose This paper aims to propose a boundary element analysis of two-dimensional linear elasticity problems by a new expanding element interpolation method. Findings The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages.
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DOI: Brezzi and L. BrezziL. Abstract We discuss the application of Virtual Elements to linear plate bending problems, in the Kirchhoff—Love formulation. As we shall see, in the Virtual Element environment the treatment of the C 1 -continuity condition is much easier than for traditional Finite Elements.
View via Publisher. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Antonietti, M. Bruggi, … M. Verani Design and convergence analysis of the conforming virtual element method for polyharmonic problems. Antonietti, G. Manzini, M. Annotations on the virtual element method for second-order elliptic problems. Manzini Citation Type. Has PDF. Publication Type. More Filters. View 1 excerpt, cites background. Research Feed. View 2 excerpts, cites background and results. View 1 excerpt, cites methods.
A multiscale virtual element method for elliptic problems in heterogeneous porous media.
Highly Influenced.This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order virtual element method VEMwith a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored.
In the latter case various options are considered for approximating the non-homogeneous fibre directions at an element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to both mild and strong non-homogeneity.
Further, the convergence rate of the VEM is shown to be comparable to classical low-order standard finite element approaches. This is a preview of subscription content, log in to check access.
Rent this article via DeepDyve. Wiley, Hoboken. Google Scholar. Wriggers P Nonlinear finite element methods. Springer, Berlin.
Virtual Element Methods for plate bending problems
Springer, New York. Hughes T The finite element method. Linear static and dynamic finite element analysis. Prentice-Hall, Englewood Cliffs. Grieshaber B, McBride A, Reddy B Uniformly convergent interior penalty methods using multilinear approximations for problems in elasticity. Comput Methods Appl Mech Eng — Math Models Methods Appl Sci 23 01 — Math Models Methods Appl Sci — Gain A, Talischi C, Paulino G On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes.
Comput Mech — Wriggers P, Hudobivnik B A low order virtual element formulation for finite elasto-plastic deformations. Wriggers P, Hudobivnik B, Korelc J Efficient low order virtual elements for anisotropic materials at finite strains.Finite Element Concepts pp Cite as. Clough Proceedings, 2nd conference on electronic computation, A.
These are plane elements with constant stress distributions. Analogous plane stress triangular elements can be similarly formulated.
To emphasize this natural extension, we first review the three-dimensional field equations of continuum mechanics, and then formulate the element stiffness matrix for triangular domains. This renders the stress and strain fields to be constant within an element.
Hence, the point-wise equilibrium is always satisfied unconditionally. Thus, it does not matter even if the linear elasticity formulations are coupled vector field problems, the shape function vectors with one zero component still qualify to be admissible functions. II as he focused on the Rayleigh—Ritz Method, just above his equation number Similar conclusions can be drawn when trapezoidal elements are used for three-dimensional linear elasticity problems. Assuming the other parts of a finite element computer program to be without any flaw, any linear stress field on arbitrary domains will be exactly reproduced irrespective of meshing details.
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From the theoretical standpoints, this observation raises a valid question as to whether other elements with more nodes will have such a property that brings the finite element method close to very reliable approximation of problems with boundaries of arbitrary shapes. Clough employed the physical concepts of virtual work to identify the entries of stiffness matrices and nodal forces to be virtual work quantities.
In: Proceedings, 2nd conference on electronic computation, A.Monogame song
Clough RW Original formulation of the finite element method.We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem. Click on title above or here to access this collection. We discuss the application of virtual elements to linear elasticity problems, for both the compressible and the nearly incompressible case. Virtual elements are very close to mimetic finite differences see, for linear elasticity, [L.
As such, they share the good features of being able to represent in an exact way certain physical properties conservation, incompressibility, etc. The advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity.
A virtual element method for transversely isotropic elasticity
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Keywords mimetic finite differencesvirtual elementselasticity.
Publication Data. Publisher: Society for Industrial and Applied Mathematics. Brezziand L.
Cited by A divergence-free reconstruction of the nonconforming virtual element method for the Stokes problem. Computer Methods in Applied Mechanics and Engineering Engineering Analysis with Boundary Elements International Journal for Numerical Methods in Engineering Advances in Computational Mathematics 46 Computational Mechanics 66 :4,Mitel ignite software
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