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An error analysis of truncated starting conditions in step‐by‐step time integration: Consequences for structural dynamics
Author(s) -
Hulbert G. M.,
Hughes T. J. R.
Publication year - 1987
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.4290150710
Subject(s) - acceleration , displacement (psychology) , dynamics (music) , mathematics , dynamic equation , numerical integration , equations of motion , mathematical analysis , control theory (sociology) , algorithm , computer science , physics , classical mechanics , nonlinear system , psychology , control (management) , quantum mechanics , artificial intelligence , acoustics , psychotherapist
Most of the step‐by‐step time integration algorithms for structural dynamics require an initial acceleration vector to be specified, in addition to displacement and velocity vectors. A consistent initial acceleration vector may be calculated by solving the equations of motion at the initial time, while a truncated initial acceleration vector is obtained by setting the acceleration values to zero. Although the truncated starting procedure decreases computational effort, it is shown to affect accuracy adversely. For the structural dynamics algorithms considered herein, the rate at which the numerical solution converges to the exact solution is O (Δ t ) when the truncated starting procedure is used, compared to O (Δ t 2 ) when consistent initial acceleration values are used.