1,721,021 research outputs found
Remarks on partial selective reduced integration method for Reissner-Mindlin plate problem
No full text
On some mixed finite element methods for plane membrane problems
No full textAn analysis of some quadrilateral dual mixed finite element methods for plane membrane problems is presented. The methods are based on a variational formulation which a priori does not involve symmetric stresses. After having presented the governing equations of the problem under discussion in the linear framework, a detailed analysis of a method already proposed in Cazzani and Atluri (1993) is performed. In particular, a result setting the equivalence of the method and another one involving symmetric stresses is established. Two other methods, this time not equivalent to any symmetric stress method, are presented and for them an analysis is outlined. Finally, some numerical tests showing the method performances are provided
Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem
No full textThe present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi:10.1007/s00466-017-1404-5), 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 viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy 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 framework
Virtual elements for the navier-stokes problem on polygonal meshes
No full textA family of virtual element methods for the two-dimensional Navier-Stokes equations is proposed and analyzed. The schemes provide a discrete velocity field which is pointwise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also performed
Asymptotic behaviour of shells of revolution in free vibration
No full textSi considera il problema di vibrazione libera per gusci di rivoluzione, con
particolare riferimento al comportamento asintotico dell’autovalore minimo, al tendere a zero
dello spessore. I risultati numerici presentati sono in accordo con le stime teoriche ottenute
mediante la teoria degli spazi di interpolazione.We consider the free vibration problem of thin shells of revolution, focusing on the
asymptotic behaviour of the lowest eigenfrequency, as the thickness tends to zero. Numerical
experiments are provided in order to confirm theoretical results obtained using interpolation
theory
A stress/displacement Virtual Element method for plane elasticity problems
No full textThe 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
On the asymptotic behaviour of shells of revolution in free vibration
No full textWe consider the free vibration problem of thin
shells of revolution of constant type of geometry, focusing
on the asymptotic behaviour of the lowest eigenfrequency,
as the thickness tends to zero. Numerical experiments are
computed using two discretization methods, collocation and
finite elements, each corresponding to a different shellmodel.
Our results are in agreement with theoretical results obtained
using interpolation theory and cited in literature
A-priori and a-posteriori error analysis for a family of Reissner-Mindlin plate elements
No full textArbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem
No full textThe 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
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