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Displacement‐controlled method and its applications to material non‐linearity
Author(s) -
Zheng H.,
Liu D. F.,
Lee C. F.,
Tham L. G.
Publication year - 2005
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.410
Subject(s) - finite element method , geomechanics , displacement (psychology) , path (computing) , simple (philosophy) , computer science , tracing , stability (learning theory) , linearity , algorithm , mathematical optimization , mathematics , calculus (dental) , structural engineering , engineering , geotechnical engineering , medicine , psychology , philosophy , electrical engineering , epistemology , dentistry , machine learning , psychotherapist , programming language , operating system
For the analysis of non‐linear problems, the displacement‐controlled method (DCM) has a more extensive application scope and more powerful abilities than the load‐controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non‐linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.