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On linear constraints for Newton–Raphson corrections and critical point searches in structural F.E. problems
Author(s) -
Eriksson Anders
Publication year - 1989
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.1620280607
Subject(s) - newton's method , finite element method , mathematics , stiffness , point (geometry) , relation (database) , mathematical optimization , iterative method , computer science , nonlinear system , geometry , physics , structural engineering , engineering , quantum mechanics , database
The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non‐linear mechanical Finite Element (F.E.) problems. An alternative to the normal two‐phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.