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Volume 5, Issue 2
Sobolev Gradient Type Preconditioning for the Saint-Venant Model of Elasto-Plastic Torsion

I. Faragό & J. Karátson

Int. J. Numer. Anal. Mod., 5 (2008), pp. 206-221.

Published online: 2008-05

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  • Abstract

In this paper a 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.

  • Keywords

elasto-plastic torsion, nonlinear elliptic problem, iterative solution, Laplacian preconditioner.

  • AMS Subject Headings

35J65, 65N30, 65H10, 74C05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-206, author = {Faragό , I. and Karátson , J.}, title = {Sobolev Gradient Type Preconditioning for the Saint-Venant Model of Elasto-Plastic Torsion}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {2}, pages = {206--221}, abstract = {

In this paper a 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/807.html} }
TY - JOUR T1 - Sobolev Gradient Type Preconditioning for the Saint-Venant Model of Elasto-Plastic Torsion AU - Faragό , I. AU - Karátson , J. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 206 EP - 221 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/807.html KW - elasto-plastic torsion, nonlinear elliptic problem, iterative solution, Laplacian preconditioner. AB -

In this paper a 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.

Faragό , I. and Karátson , J.. (2008). Sobolev Gradient Type Preconditioning for the Saint-Venant Model of Elasto-Plastic Torsion. International Journal of Numerical Analysis and Modeling. 5 (2). 206-221. doi:
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