68 research outputs found
Numerical results for mimetic discretization of Reissner-Mindlin plate problems
A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate
problems is considered. Together with the source problem, the free vibration
and the buckling problems are investigated. Full details about the scheme
implementation are provided, and the numerical results on several different
types of meshes are reported
A Dual Hybrid Virtual Element Method for Plane Elasticity Problems
A dual hybrid Virtual Element scheme for plane linear elastic problems is
presented and analysed. In particular, stability and convergence results have
been established. The method, which is first order convergent, has been
numerically tested on two benchmarks with closed form solution, and on a
typical microelectromechanical system. The numerical outcomes have proved that
the dual hybrid scheme represents a valid alternative to the more classical
low-order displacement-based Virtual Element Method
Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem
The present paper is the second part of a twofold work, whose first part is
reported in [3], concerning a newly developed Virtual Element Method (VEM) for
2D continuum problems. The first part of the work proposed a study for linear
elastic problem. The aim of this part is to explore the features of the VEM
formulation when material nonlinearity is considered, showing that the accuracy
and easiness of implementation discovered in the analysis inherent to the first
part of the work are still retained. Three different nonlinear constitutive
laws are considered in the VEM formulation. In particular, the generalized
viscoplastic model, the classical Mises plasticity with isotropic/kinematic
hardening and a shape memory alloy (SMA) constitutive law are implemented. The
versatility with respect to all the considered nonlinear material constitutive
laws is demonstrated through several numerical examples, also remarking that
the proposed 2D VEM formulation can be straightforwardly implemented as in a
standard nonlinear structural finite element method (FEM) framework
An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
In this paper, we derive and analyze a Reissner-Mindlin-like model
for isotropic heterogeneous linearly elastic plates.
The modeling procedure is based on a Hellinger-Reissner principle,
which we modify to derive consistent models.
Due to the material heterogeneity, the classical polynomial profiles
for the plate shear stress are replaced by more sophisticated choices,
that are asymptotically correct.
In the homogeneous case we recover a Reissner-Mindlin model
with 5/6 as shear correction factor.
Asymptotic expansions are used to estimate the modeling error. We remark that our derivation is not based on asymptotic
arguments only.
Thus, the model obtained is more sophisticated (and accurate) than
simply taking the asymptotic limit of the three dimensional problem.
Moreover, we do not assume periodicity of the heterogeneities
A lowest order stabilization-free mixed Virtual Element Method
We initiate the design and the analysis of stabilization-free Virtual Element
Methods for the laplacian problem written in mixed form. A Virtual Element
version of the lowest order Raviart-Thomas Finite Element is considered. To
reduce the computational costs, a suitable projection on the gradients of
harmonic polynomials is employed. A complete theoretical analysis of stability
and convergence is developed in the case of quadrilateral meshes. Some
numerical tests highlighting the actual behaviour of the scheme are also
provided
A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics
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
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