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A family of solution algorithms for nonlinear structural analysis based on relaxation equations
Author(s) -
Park K. C.
Publication year - 1982
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.1620180906
Subject(s) - nonlinear system , algorithm , mathematics , relaxation (psychology) , homotopy perturbation method , bifurcation , limit point , newton's method , homotopy , computer science , mathematical analysis , pure mathematics , psychology , social psychology , physics , quantum mechanics
A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko‐Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by‐product of the algorithms is that they provide a systematic and economical means for computing the stepsize at each iteration stage when a Newton‐like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.