scholarly journals Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

2021 ◽  
Vol 383 ◽  
pp. 113917
Author(s):  
Andrea Borio ◽  
François P. Hamon ◽  
Nicola Castelletto ◽  
Joshua A. White ◽  
Randolph R. Settgast
Keyword(s):  
Finite Difference ◽  
Element Formulation ◽  
Virtual Element

scholarly journals Virtual element formulation for isotropic damage

2018 ◽  
Vol 144 ◽  
pp. 38-48 ◽  
Author(s):  
Maria Laura De Bellis ◽  
Peter Wriggers ◽  
Blaž Hudobivnik ◽  
Giorgio Zavarise
Keyword(s):  
Element Formulation ◽  
Isotropic Damage ◽  
Virtual Element

A Simple Total-Lagrangian Finite-Element Formulation for Nonlinear Behavior of Planar Beams

2018 ◽  
Author(s):  
Enrico Babilio ◽  
Stefano Lenci
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Finite Difference ◽  
Shear Angle ◽  
Difference Schemes ◽  
Finite Element Formulation ◽  
Finite Difference Schemes ◽  
Element Formulation ◽  
Beam Model ◽  
Lagrangian Finite Element

The present contribution reports some preliminary results obtained applying a simple finite element formulation, developed for discretizing the partial differential equations of motion of a novel beam model. The theoretical model we are dealing with is geometrically exact, with some peculiarities in comparison with other existing models. In order to study its behavior, some numerical investigations have already been performed through finite difference schemes and other methods and are reported in previous contributions. Those computations have enlightened that the model under analysis turns out to be quite hard to handle numerically, especially in dynamics. Hence, we developed ad hoc the total-lagrangian finite-element formulation we report here. The main differences between the theoretical model and its numerical formulation rely on the fact that in the latter the absolute value of the shear angle is assumed to remain much smaller than unity, and strains are piecewise constant along the beam. The first assumption, which actually simplifies equations, has been taken on the basis of results from previous integrations, mainly through finite difference schemes, which clearly showed that, while other strains can achieve large values in their range of admissibility, shear angle actually remains small. The second assumption led us to define a two-nodes constant-strain finite element, with a fast convergence, in terms of number of elements versus solution accuracy. Although, at the present stage of this ongoing research, we have only early results from finite elements, they appear encouraging and start to shed new light on the behavior of the beam model under analysis.

Analysis of Elastic-Plastic Impact Involving Severe Distortions

1976 ◽  
Vol 43 (3) ◽  
pp. 439-444 ◽  
Author(s):  
G. R. Johnson
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Triangular Element ◽  
Element Formulation ◽  
Lagrangian Analysis ◽  
Triangular Finite Element ◽  
Elastic Plastic ◽  
Analysis Technique ◽  
Difference Methods ◽  
Impact Problems

A Lagrangian analysis technique is presented for two-dimensional axi-symmetric impact problems involving elastic-plastic flow. This technique is based on a triangular finite-element formulation rather than the quadrilateral formulation generally used in comparable finite-difference methods. For impact problems involving severe distortions, the triangular element formulation is better suited to represent the severe distortions than is the traditional quadrilateral finite-difference method. Included are the formulation of the technique and illustrative examples.

Finite Difference Modeling of Anisotropic Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 458-464 ◽  
Author(s):  
M. Keyhani ◽  
R. A. Polehn
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Taylor Expansion ◽  
Control Volume ◽  
Element Formulation ◽  
Solution Stability ◽  
The Finite Element Method ◽  
Finite Difference Equations ◽  
Anisotropic Heat Conduction ◽  
Limiting Case

A modification to the finite difference equations is proposed in modeling multidimensional flows in an anisotropic material. The method is compared to the control volume version of the Taylor expansion and the finite element formulation derived from the Galerkin weak statement. For the same number of nodes, the proposed finite difference formulation approaches the accuracy of the finite element method. For the two-dimensional case, the effect on accuracy and solution stability is approximately the same as quadrupling the number of nodes for the Taylor expansion with only a proportionately small increase in the number of computations. Excellent comparisons are made with a new limiting case exact solution modeling anisotropic heat conduction and a transient, anisotropic conduction experiment from the literature.

scholarly journals Virtual Element Formulation for Finite Strain Elastodynamics

2021 ◽  
Vol 129 (3) ◽  
pp. 1151-1180
Author(s):  
Mertcan Cihan ◽  
BlaŽ Hudobivnik ◽  
Fadi Aldakheel ◽  
Peter Wriggers
Keyword(s):  
Finite Strain ◽  
Element Formulation ◽  
Virtual Element

scholarly journals First-order VEM for Reissner–Mindlin plates

2021 ◽  
Author(s):  
A. M. D’Altri ◽  
L. Patruno ◽  
S. de Miranda ◽  
E. Sacco
Keyword(s):  
Stiffness Matrix ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Virtual Element Method ◽  
First Order ◽  
Independent Variables ◽  
Virtual Element ◽  
Displacement Based

AbstractIn this paper, a first-order virtual element method for Reissner–Mindlin plates is presented. A standard displacement-based variational formulation is employed, assuming transverse displacement and rotations as independent variables. In the framework of the first-order virtual element, a piecewise linear approximation is assumed for both displacement and rotations on the boundary of the element. The consistent term of the stiffness matrix is determined assuming uncoupled polynomial approximations for the generalized strains, with different polynomial degrees for bending and shear parts. In order to mitigate shear locking in the thin-plate limit while keeping the element formulation as simple as possible, a selective scheme for the stabilization term of the stiffness matrix is introduced, to indirectly enrich the approximation of the transverse displacement with respect to that of the rotations. Element performance is tested on various numerical examples involving both thin and thick plates and different polygonal meshes.

Serendipity virtual element formulation for nonlinear elasticity

2019 ◽  
Vol 223 ◽  
pp. 106094 ◽  
Author(s):  
M.L. De Bellis ◽  
P. Wriggers ◽  
B. Hudobivnik
Keyword(s):  
Nonlinear Elasticity ◽  
Element Formulation ◽  
Virtual Element

scholarly journals A virtual element formulation for general element shapes

2020 ◽  
Vol 66 (4) ◽  
pp. 963-977 ◽  
Author(s):  
P. Wriggers ◽  
B. Hudobivnik ◽  
F. Aldakheel
Keyword(s):  
Considerable Progress ◽  
Element Formulation ◽  
Virtual Element Method ◽  
Polynomial Degree ◽  
General Element ◽  
Arbitrary Polynomial ◽  
Arbitrary Geometries ◽  
Virtual Element ◽  
Element Method

Abstract The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.

Sign in / Sign up

Export Citation Format

Share Document