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Convergence analysis and validation of sequential limit analysis of plane‐strain problems of the von Mises model with non‐linear isotropic hardening
Author(s) -
Leu S.Y.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1367
Subject(s) - von mises yield criterion , mathematics , isotropy , limit analysis , plane stress , limit (mathematics) , smoothing , upper and lower bounds , mathematical analysis , mathematical optimization , finite element method , structural engineering , statistics , engineering , physics , quantum mechanics
The paper presents sequential limit analysis of plane‐strain problems of the von Mises model with non‐linear isotropic hardening by using a general algorithm. The general algorithm is a combined smoothing and successive approximation (CSSA) method. In the paper, emphasis is placed on its convergence analysis and validation applied to sequential limit analysis involving materials with isotropic hardening. By sequential limit analysis, the paper treats deforming problems as a sequence of limit analysis problems stated in the upper bound formulation. Especially, the CSSA algorithm was proved to be unconditionally convergent by utilizing the Cauchy–Schwarz inequality. Finally, rigorous validation was conducted by numerical and analytical studies of a thick‐walled cylinder under pressure. It is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions. Copyright © 2005 John Wiley & Sons, Ltd.