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Using eigenvector projections to improve convergence in non‐linear finite element equilibrium iterations
Author(s) -
Eriksson Anders
Publication year - 1987
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.1620240303
Subject(s) - eigenvalues and eigenvectors , dynamic relaxation , convergence (economics) , finite element method , stability (learning theory) , displacement (psychology) , buckling , mathematics , relaxation (psychology) , projection (relational algebra) , mathematical optimization , variable (mathematics) , inverse iteration , iterative method , relation (database) , computer science , algorithm , mathematical analysis , structural engineering , geometry , psychology , social psychology , physics , economics , psychotherapist , economic growth , database , quantum mechanics , machine learning , engineering
In an earlier paper a method for calculation of non‐linear structural response was described. The method is based on an algorithm, proposed by Bergan, including simultaneous iterations in the load and displacement spaces. A method for selective damping of solution components parallel to critical eigenvectors was proposed reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the ‘dynamic relaxation’ approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N–R schemes. The extra computational effort is considered worth while in cases where restarts in the calculation are not desired. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.