Journal ArticleDOI
Local and global smoothing of discontinuous finite element functions using a least squares method
E. Hinton,John S. Campbell +1 more
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In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.Abstract:
The concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.
The relationship between local smoothing and the ‘reduced’ integration' technique is established.
Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.
The paper concludes with some practical recommendations for discontinuous finite element function smoothing.read more
Citations
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Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this article, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes, which has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems.
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this paper, the authors derived a theorem showing the dependence of the effectivity index for the Zienkiewicz-Zhu error estimator on the convergence rate of the recovered solution.
Book
Introduction to finite element vibration analysis
TL;DR: In this article, the finite element displacement method was used for the analysis of free vibration of plates and shells, and for the simulation of forced response and forced response analysis of rigid and flexible plates.
Journal ArticleDOI
Multiscale Methods for Composites: A Review
TL;DR: In this article, a review of multiscale methods for modeling mechanical and thermomechanical responses of composites is presented, both at the material level and at the structural analysis level.
Journal ArticleDOI
Elastic contact versus indentation modeling of multi-layered materials
TL;DR: In this paper, the elastic contact problem of a rigid cylindrical punch indenting a multi-layered linear elastic half space is studied and then used to model the unloading phase of a microindentation test of thin fims deposited on a substrate.
References
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Journal ArticleDOI
Reduced integration technique in general analysis of plates and shells
TL;DR: In this article, a simple extension is made which allows the element to be economically used in all situations by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties.
Book
Finite Elements of Nonlinear Continua
TL;DR: The Methode des elements finis reference record was created on 2004-09-07, modified on 2016-08-08 as mentioned in this paper, and was used for the reference record.
Journal ArticleDOI
On the calculation of consistent stress distributions in finite element approximations
J. T. Oden,H. J. Brauchli +1 more
TL;DR: In this paper, the theory of conjugate approximations is used to obtain persistent approximation of stress fields in finite element approximation based on displacement and assumptions, and these consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
Journal ArticleDOI
Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressures
TL;DR: In this paper, a displacement method was used to assess the stress accuracy at very low compressibilities. But the authors found that the mean stress becomes grossly in error at the center and edges of each element as the compressibility is reduced whereas the deviatoric stress components do not.
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The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
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