Convergence of the Newton‐Raphson algorithm in elastic‐plastic incremental analysis
作者:
S. Caddemi,
J. B. Martin,
期刊:
International Journal for Numerical Methods in Engineering
(WILEY Available online 1991)
卷期:
Volume 31,
issue 1
页码: 177-191
ISSN:0029-5981
年代: 1991
DOI:10.1002/nme.1620310110
出版商: John Wiley&Sons, Ltd
数据来源: WILEY
摘要:
AbstractA spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method. This assumption permits the incremental problem to be formulated as a convex non‐linear programming problem. The classical Newton‐Raphson algorithm can be adopted to provide an iterative solution of the non‐linear programming problem. It is shown that if an elastic or secant predictor modulus is used, the algorithm converges monotonically. However, if a tangent predictor is used, a line search algorithm must be included to ensure conver
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