Iterative solution of mixed problems and the stress recovery procedures

Zienkiewicz, O. C.; Li, Xikui; Nakazawa, S.

doi:10.1002/cnm.1630010103

Cited by 45 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a consequence, the results are not substantially better than what one would obtain using a displacement method with the same displacement approximations as those used in the mixed method. Let us also point out that the good results reported [19,27] with some methods of this type are apparently due to the rectangular meshes used. For rectangular meshes it is known that certain "superapproximation" phenomenon will occur, cf.…”

Section: Introductionmentioning

confidence: 91%

A family of mixed finite elements for the elasticity problem

Stenberg¹

1988

Numer. Math.

289

212

View full text Add to dashboard Cite

Summary.A new mixed finite element formulation for the equations of linear elasticity is considered. In the formulation the variables approximated are the displacement, the unsymmetric stress tensor and the rotation. The rotation act as a Lagrange multiplier introduced in order to enforce the symmetry of the stress tensor. Based on this formulation a new family of both twoand three-dimensional mixed methods is defined. Optimal error estimates, which are valid uniformly with respect to the Poisson ratio, are derived. Finally, a new postprocessing scheme for improving the displacement is introduced and analyzed.

show abstract

Section: Introductionmentioning

confidence: 91%

A family of mixed finite elements for the elasticity problem

Stenberg¹

1988

Numer. Math.

289

212

View full text Add to dashboard Cite

show abstract

“…[57]. Other procedures for nodal stress recovery can also be found in the literature, including global projection [58] and extraction and other alternatives [59]. In all the above-mentioned nodal stress recovery methods, the nodal stresses obtained, are generally not superconvergent.…”

Section: Finite Elementmentioning

confidence: 99%

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Ullah

Coombs

Augarde

2013

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

'An adaptive nite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems.', Computer methods in applied mechanics and engineering., 267 . pp. 111-132. Further information on publisher's website:http://dx.doi.org/10.1016/j.cma.2013.07.018Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 267, 2013, 10.1016/j.cma.2013.07.018. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an EFG zone. This EFG zone can be further refined by adding nodes, thus avoiding computationally expensive FE remeshing. Local maximum entropy shape functions are used in the EFG zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the EFG and FE regions compared to the use of moving least squares basis functions. The Zienkiewicz & Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region.

show abstract

“…However the evaluation of the spatial gradient of φ requires an -at least -C 0 continuous approximation of the quantity φ that for instance can be obtained by a least-squares interpolation (see e.g. [69]). The vector of nodal valuesφ = [φ I ] is determined from the values at the integration pointsφ according to the following implicit equation…”

Section: Direct Solution Scheme For the Advection Equationmentioning

confidence: 99%

Advection approaches for single- and multi-material arbitrary Lagrangian–Eulerian finite element procedures

Fressmann¹,

Wriggers

2005

Comput Mech

View full text Add to dashboard Cite

The essential feature in arbitrary Lagrangian-Eulerian (ALE) based finite element approaches is the additional requirement to consider flow effects of the materials and the solution variables through the computational domain. These flow effects are commonly known as advective effects. The present paper examines different advection strategies for the application of the ALE finite element method in a finite deformation solid mechanics framework, where especially micromechanical problems are referred to. The global solution algorithm is based on the well-known fractional step method that provides an operator splitting approach for the solution of the coupled ALE equations. Distinguishing the so-called single-material and the multi-material ALE method, different advection schemes based on volume-and material-associated advection procedures are required. For the latter case, the material interfaces are not resolved explicitly by the finite element mesh. Instead a volume-of-fluid interface tracking approach in terms of the volume fractions of the different material phases is applied.

show abstract

Iterative solution of mixed problems and the stress recovery procedures

Cited by 45 publications

References 6 publications

A family of mixed finite elements for the elasticity problem

A family of mixed finite elements for the elasticity problem

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Advection approaches for single- and multi-material arbitrary Lagrangian–Eulerian finite element procedures

Contact Info

Product

Resources

About