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Derivatives of tangential stiffness matrices for equilibrium path descriptions
Author(s) -
Eriksson Anders
Publication year - 1991
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.1620320511
Subject(s) - stiffness , bifurcation , mathematics , stiffness matrix , stability (learning theory) , finite element method , element (criminal law) , direct stiffness method , matrix (chemical analysis) , path (computing) , basis (linear algebra) , numerical analysis , mathematical analysis , computer science , geometry , structural engineering , nonlinear system , engineering , physics , materials science , quantum mechanics , machine learning , law , political science , composite material , programming language
The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non‐linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step‐wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post‐bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.