Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions
نویسندگان
چکیده
The date of receipt and acceptance will be inserted by the editor Summary We construct stable, conforming and symmetric finite elements for the mixed formulation of the linear elasticity problem in two dimensions. In our approach we add three divergence free rational functions to piecewise polynomials to form the stress finite element space. The relation with the elasticity elements and a class of generalized C 1 Zienkiewicz elements is also discussed.
منابع مشابه
Lower Order Finite Element Approximations of Symmetric Tensors on Simplicial Grids in R
In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div) − Pk (1 ≤ k ≤ n) tensor spaces, enriched, for each n − 1 dimensional simplex, by (n+1)n 2 H(div) − Pn+1 bubble functions when 1 ≤ k ≤ n − 1, and by (n−1)n 2 H(di...
متن کاملA Family of Conforming Mixed Finite Elements for Linear Elasticity on Triangular Grids
This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full C0-Pk space enriched by (k − 1) H(div) edge bubble functions on each internal edge, while the displacement field by the full discontinuous Pk−1 vector-valued...
متن کاملNon Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...
متن کاملSymmetric Nonconforming Mixed Finite Elements for Linear Elasticity
We present a family of mixed methods for linear elasticity, that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces,...
متن کاملNon-conforming Computational Methods for Mixed Elasticity Problems
Abstract — In this paper, we present a non-conforming hp computational modeling methodology for solving elasticity problems. We consider the incompressible elasticity model formulated as a mixed displacement-pressure problem on a global domain which is partitioned into several local subdomains. The approximation within each local subdomain is designed using div-stable hp-mixed finite elements. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Numerische Mathematik
دوره 126 شماره
صفحات -
تاریخ انتشار 2014