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

Daniel, WJT (2003) Explicit/implicit partitioning and a new explicit form of the generalized alpha method. Communications In Numerical Methods In Engineering, 19 11: 909-920. doi:10.1002/cnm.640

Author Daniel, WJT
Title Explicit/implicit partitioning and a new explicit form of the generalized alpha method
Journal name Communications In Numerical Methods In Engineering   Check publisher's open access policy
ISSN 1069-8299
Publication date 2003-01-01
Sub-type Article (original research)
DOI 10.1002/cnm.640
Volume 19
Issue 11
Start page 909
End page 920
Total pages 12
Place of publication W Sussex, England
Publisher John Wiley & Sons Ltd
Language eng
Subject C1
230113 Dynamical Systems
780102 Physical sciences
Abstract 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-alpha algorithm 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-alpha method. 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 (C) 2003 John Wiley Sons, Ltd.
Keyword Mathematics, Interdisciplinary Applications
Engineering, Multidisciplinary
Direct Integration
Finite Elements
Explicit/implicit Partition
Generalized Alpha Method
Improved Numerical Dissipation
Time Integration Algorithms
Structural Dynamics
Transient Analysis
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Created: Wed, 15 Aug 2007, 05:28:02 EST