26 research outputs found
Virtual Element Method for fourth order problems: estimates
We analyse the family of -Virtual Elements introduced in
\cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal
estimates in and in via classical duality arguments
Rotating Electromagnetic Waves in Toroid-Shaped Regions
Electromagnetic waves, solving the full set of Maxwell equations in vacuum,
are numerically computed. These waves occupy a fixed bounded region of the
three dimensional space, topologically equivalent to a toroid. Thus, their
fluid dynamics analogs are vortex rings. An analysis of the shape of the
sections of the rings, depending on the angular speed of rotation and the major
diameter, is carried out. Successively, spherical electromagnetic vortex rings
of Hill's type are taken into consideration. For some interesting peculiar
configurations, explicit numerical solutions are exhibited.Comment: 27 pages, 40 figure
Remarks on some mixed finite element schemes for Reissner--Mindlin plate model
Two different stabilization procedures for mixed finite element
schemes for Reissner--Mindlin plate problems are introduced. They are based on
a suitable modification of the discrete shear energy like that introduced when
a partial selective reduced integration technique is used. Some numerical
results will be presented in order to show the performance of these schemes
with respect to the locking phenomenon. The dependence of the approximate
solution on the stabilising parameter is also analized
Approximation of functionally graded plates with non-conforming finite elements
In this paper rectangular plates made of functionally graded materials (FGMs) are studied. A two-constituent material distribution through the thickness is considered, varying with a simple power rule of mixture. The equations governing the FGM plates are determined using a variational formulation arising from the Reissner-Mindlin theory. To approximate the problem a simple locking-free Discontinuous Galerkin finite element of non-conforming type is used, choosing a piecewise linear non-conforming approximation for both rotations and transversal displacement. Several numerical simulations are carried out in order to show the capability of the proposed element to capture the properties of plates of various gradings, subjected to thermo-mechanical loads. (C) 2006 Elsevier B.V. All rights reserved
Penalized approximation of the vibration frequencies of a fluid in a cavity
Here we point out some difficulties arising in the approximation of
the vibration frequencies of a fluid in a cavity in the case of non convex
polygonal domains. Since the eigensolutions must satisfy an irrotationality
condition, a classical way to face the problem is to consider a penalized
formulation. Unfortunately standard conforming finite elements fail to give
good results. We intend to justify this failure and to suggest a finite element
method based on a reduced integration strategy able to give reasonable results
MITC9 shell elements based on refined theories for the analysis of isotropic cylindrical structures
In this work a nine-nodes shell finite element, formulated in the framework of Carrera’s Unified Formulation (CUF), is presented. The exact geometry of cylindrical shells is considered. The Mixed Interpolation of Tensorial Components (MITC) technique is applied to the element in order to overcome shear and membrane locking phenomenon. High-order equivalent single layer theories contained in the CUF are used to perform the analysis of shell structures. Benchmark solutions from the open literature are taken to validate the obtained results. The mixed-interpolated shell finite element shows good properties of convergence and robustness by increasing the number of used elements and the order of expansion of displacements in the thickness direction