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Numerical stability of dynamic relaxation analysis of non‐linear structures
Author(s) -
Cassell A. C.,
Hobbs R. E.
Publication year - 1976
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.1620100620
Subject(s) - dynamic relaxation , mathematics , stability (learning theory) , relaxation (psychology) , stiffness , convergence (economics) , axial symmetry , constant (computer programming) , stiffness matrix , iterative method , matrix (chemical analysis) , direct stiffness method , numerical analysis , beam (structure) , variable (mathematics) , mathematical analysis , mathematical optimization , geometry , structural engineering , computer science , materials science , engineering , psychology , social psychology , machine learning , economics , composite material , programming language , economic growth
Abstract The estimation of the parameters (‘fictitious densities’) which control the convergence and numerical stability of a non‐linear Dynamic Relaxation solution is described. The optimal values of these parameters vary during the iterative solution and they are predicted from the Gerschgörin bounds, that is rowsums of the stiffness matrix, which are divided into constant and variable parts for computational convenience. The procedure is illustrated by reference to the analysis of an axially loaded beam on a non‐uniform elastic foundation.