Tao Xue¹, Yazhou Wang², Masao Shimada², David Tae², Kumar Tamma^2,*, Xiaobing Zhang^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 1469-1487, 2023, DOI:10.32604/cmes.2022.021616

Abstract In this work, a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented. The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement. Several numerical examples have been used to validate the proposed tangential displacement evaluation; this is in contrast to past practices which only seem to attain the first-order time accuracy… More >

R.Kanapady¹, K.K.Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 103-118, 2003, DOI:10.3970/cmes.2003.004.103

Abstract Of general interest here is the time dimension aspect wherein discretized operators in time may be continuous or discontinuous; and of particular interest and focus here is the design of time discretized operators in the context of discontinuous state-phase for computational dynamics applications. Based on a generalized bi-discontinuous time weighted residual formulation, the design leading to a new unified set of hierarchical energy conserving and energy dissipating time discretized operators are developed for the first time that are fundamentally useful for time adaptive computations for dynamic problems. Unlike time discontinuous Galerkin approaches, the design is based upon a time discontinuous… More >