12,296 research outputs found
A Virtual Element Method for elastic and inelastic problems on polytope meshes
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and
inelastic problems, mainly focusing on a small deformation regime. The
numerical scheme is based on a low-order approximation of the displacement
field, as well as a suitable treatment of the displacement gradient. The
proposed method allows for general polygonal and polyhedral meshes, it is
efficient in terms of number of applications of the constitutive law, and it
can make use of any standard black-box constitutive law algorithm. Some
theoretical results have been developed for the elastic case. Several numerical
results within the 2D setting are presented, and a brief discussion on the
extension to large deformation problems is included
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
A Stress/Displacement Virtual Element Method for Plane Elasticity Problems
The numerical approximation of 2D elasticity problems is considered, in the
framework of the small strain theory and in connection with the mixed
Hellinger-Reissner variational formulation. A low-order Virtual Element Method
(VEM) with a-priori symmetric stresses is proposed. Several numerical tests are
provided, along with a rigorous stability and convergence analysis
Nonconforming tetrahedral mixed finite elements for elasticity
This paper presents a nonconforming finite element approximation of the space
of symmetric tensors with square integrable divergence, on tetrahedral meshes.
Used for stress approximation together with the full space of piecewise linear
vector fields for displacement, this gives a stable mixed finite element method
which is shown to be linearly convergent for both the stress and displacement,
and which is significantly simpler than any stable conforming mixed finite
element method. The method may be viewed as the three-dimensional analogue of a
previously developed element in two dimensions. As in that case, a variant of
the method is proposed as well, in which the displacement approximation is
reduced to piecewise rigid motions and the stress space is reduced accordingly,
but the linear convergence is retained.Comment: 13 pages, 2 figure
Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft
- …