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. 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.

Biodegradation and ecotoxicity evaluation of a bionolle and starch blend and its degradation products in compost

A polymer based on a blend of starch and Bionolle(TM) has been prepared and tested for biodegradation in compost. The polymer was completely mineralised to carbon dioxide in 45 days. The potential toxicity of the polymer was tested against the earthworm Eisenia fetida using a modification of the American Standard for Testing Materials E1976-97. The earthworms were exposed to 30 g of the polymer for 28 days and changes in weight recorded. In addition, the polymer was firstly degraded by the compost and the worms exposed to the breakdown products for 28 days. Differences in weight were also recorded. In each case the production of juveniles was noted and all earthworms were examined for pathology. The results obtained were processed statistically using a t-test. The number of juveniles, produced from the breakdown products, was highly significant (P < 0.001) when compared to the earthworms added to the intact polymer. There was a definitely significant difference (P < 0.01, t = 3.25) in change in weight between the earthworms that were exposed to the polymer directly and those that were exposed to the breakdown products. There was no indication of any pathology of any earthworms. The polymer is considered safe for this species. (C) 2002 Elsevier Science Ltd. All rights reserved.

The application of wave induced forces to a two-dimensional finite element long wave hydrodynamic model

This paper describes the modification of a two-dimensional finite element long wave hydrodynamic model in order to predict the net current and water levels attributable to the influences of waves. Tests examine the effects of the application of wave induced forces, including comparisons to a physical experiment. An example of a real river system is presented with comparisons to measured data, which demonstrate the importance of simulating the combined effects of tides and waves upon hydrodynamic behavior. (C) 2002 Elsevier Science Ltd. All rights reserved.