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Discussion of “development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation” by Chinmoy Kolay and James M. Ricles
Author(s) -
Maxam Dean J.,
Tamma Kumar K.
Publication year - 2018
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.3133
Subject(s) - dissipation , solver , factorization , mathematics , stiffness , direct integration of a beam , class (philosophy) , stability (learning theory) , stiffness matrix , relation (database) , algorithm , computer science , mathematical optimization , engineering , structural engineering , physics , thermodynamics , database , machine learning , artificial intelligence
Summary The time integration method proposed by Kolay and Ricles, which was claimed to be both explicit and unconditionally stable, is shown to be implicit in the sense of requiring the factorization of an effective stiffness matrix where an explicit method needs no solver. Its original derivation procedure employed discrete control theory concepts, which are in fact, equivalent to conventional recurrence relation concepts aiming to match its spectral properties with those of the three‐parameter optimal/generalized‐ α method, thus giving rise to an implicit method within the class of linear multistep methods. It is shown that the resulting method possesses several added computational drawbacks due to its derivation procedure, such as additional effective stiffness inversions and a degraded order of accuracy in general.