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Tracing the equilibrium path by dynamic relaxation in materially nonlinear problems
Author(s) -
Siddiquee M. S. A.,
Tanaka T.,
Tatsuoka F.
Publication year - 1995
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.1610191102
Subject(s) - nonlinear system , dynamic relaxation , tracing , displacement (psychology) , relaxation (psychology) , convergence (economics) , linearity , finite element method , trace (psycholinguistics) , granular material , mathematics , control theory (sociology) , mechanics , computer science , structural engineering , engineering , physics , geometry , geotechnical engineering , control (management) , artificial intelligence , psychotherapist , economic growth , operating system , psychology , social psychology , quantum mechanics , electrical engineering , economics , philosophy , linguistics
Material non‐linearity in non‐associated high friction materials exhibiting post‐peak softening such as granular materials poses a great problem in solving the non‐linear differential equations. In this regard, a dynamic relaxation (DR) family of solutions provides a very strong tool to solve. In this paper, the DR method is evaluated from the viewpoint of its ability to trace the whole equilibrium curve in the load–displacement (stress–strain) space. In the case of material non‐linearity, usually there is a snap‐through. This problem has been handled in three ways: (1) load control with a real time dynamic solution at post‐peak, (2) direct displacement control and (3) arc‐length control. These three methods of non‐linear equilibrium path tracing are critically evaluated with respect to their speed of convergence, accuracy of the solution and states of unequilibrium. Finally, the results of multi‐element FEM simulations of a bearing capacity test of a strip footing on sand carried out to validate the DR methods are presented.