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An orthogonal residual procedure for non‐linear finite element equations
Author(s) -
Krenk Steen
Publication year - 1995
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.1620380508
Subject(s) - orthogonality , residual , mathematics , finite element method , displacement (psychology) , conjugate gradient method , mathematical analysis , scaling , limit (mathematics) , method of mean weighted residuals , mathematical optimization , geometry , algorithm , structural engineering , engineering , psychology , galerkin method , psychotherapist
A general and robust solution procedure for non‐linear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state. The method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector. The orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters. Passage of load and displacement limit points is discussed as well as the relation to line search, minimum residual, and are‐length methods. The method is illustrated by two examples.