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Solution techniques for non−linear finite element problems
Author(s) -
Bergan P. G.,
Horrigmoe G.,
Bråkeland B.,
Søreide T. H.
Publication year - 1978
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.1620121106
Subject(s) - finite element method , mathematics , scalar (mathematics) , stiffness , simple (philosophy) , mathematical optimization , computer science , algorithm , engineering , structural engineering , geometry , philosophy , epistemology
The paper presents a classification of mathematical commonly encountered in connection with solution of non−linear finite element problems. The principal methods for numerical solution of the non−linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap−through and snap−back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non−linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several examples.