Sobolev gradient type preconditioning for the saint-venant model of elasto-plastic torsion

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3 Citations (Scopus)

Abstract

In this paper suitable Laplacian preconditioner is proposed for the numerical solution of the nonlinear elasto-plastic torsion problem. The aim is to determine the tangential stress in cross-sections under a given torsion, for which the physical model is based on the Saint Venant model of torsion and the single curve hypothesis for the connection of strain and stress. The proposed iterative solution of the arising nonlinear elliptic problem is achieved by combining the advantages of Laplacian preconditioners with the qualitatively favourable aspects of the strong formulation. Error estimate is given for the convergence of the method. Finally, a numerical example is given.

Original languageEnglish
Pages (from-to)206-221
Number of pages16
JournalInternational Journal of Numerical Analysis and Modeling
Volume5
Issue number2
Publication statusPublished - 2008

Fingerprint

Sobolev Gradient
Elasto-plastic
Preconditioning
Torsional stress
Torsion
Plastics
Preconditioner
Nonlinear Elliptic Problems
Iterative Solution
Physical Model
Error Estimates
Cross section
Numerical Solution
Model
Numerical Examples
Curve
Formulation

Keywords

  • Elasto-plastic torsion
  • Iterative solution
  • Laplacian preconditioner
  • Nonlinear elliptic problem

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

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AU - Karátson, J.

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AB - In this paper suitable Laplacian preconditioner is proposed for the numerical solution of the nonlinear elasto-plastic torsion problem. The aim is to determine the tangential stress in cross-sections under a given torsion, for which the physical model is based on the Saint Venant model of torsion and the single curve hypothesis for the connection of strain and stress. The proposed iterative solution of the arising nonlinear elliptic problem is achieved by combining the advantages of Laplacian preconditioners with the qualitatively favourable aspects of the strong formulation. Error estimate is given for the convergence of the method. Finally, a numerical example is given.

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KW - Nonlinear elliptic problem

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