EXPLICIT/IMPLICIT PARTITIONING OF THE GENERALIZED ALPHA METHOD

Abstract

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. However, their algorithms use incompatible parameter sets and cannot be used together in an implicit/explicit spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-α 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 be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-α method.