Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method....

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Vydané v:	Communications in numerical methods in engineering Ročník 19; číslo 11; s. 909 - 920
Hlavný autor:	Daniel, W. J. T.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Chichester, UK John Wiley & Sons, Ltd 01.11.2003 Wiley
Predmet:	Computational techniques direct integration Exact sciences and technology explicit/implicit partition finite elements Finite-element and galerkin methods Fundamental areas of phenomenology (including applications) generalized alpha method Mathematical methods in physics Physics Solid mechanics Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Vibrations and mechanical waves generalized alpha method explicit/implicit partition direct integration finite elements
ISSN:	1069-8299, 1099-0887
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Popis
Shrnutí:	Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non‐linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT‐αalgorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT‐αmethod. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid‐point of a cycle. Copyright © 2003 John Wiley & Sons, Ltd.
Bibliografia:	istex:B71C4BA58B738737299E674455640718A078EDA5 ArticleID:CNM640 ark:/67375/WNG-26ZDZ8XT-6 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1069-8299 1099-0887
DOI:	10.1002/cnm.640