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.

Quadriceps activation in closed and in open kinetic chain exercise

Purpose: For treatment of various knee disorders, muscles are trained in open or closed kinetic chain tasks. Coordination between the heads of the quadriceps muscle is important for stability and optimal joint loading for both the tibiofemoral and the patellofemoral joint. The aim of this study was to examine whether the quadriceps femoris muscles are activated differently in open versus closed kinetic chain tasks. Methods: Ten healthy men and women (mean age 28.5 +/- 0.7) extended the knees isometrically in open and closed kinetic chain tasks in a reaction time paradigm using moderate force. Surface electromyography (EMG) recordings were made from four different parts of the quadriceps muscle. The onset and amplitude of EMG and force data were measured. Results: In closed chain knee extension, the onset of EMG activity of the four different muscle portions of the quadriceps was more simultaneous than in the open chain. In open chain, rectus femoris (RF) had the earliest EMG onset while vastus medialis obliquus was activated last (7 +/- 13 ms after RF EMG onset) and with smaller amplitude (40 +/- 30% of maximal voluntary contraction (MVC)) than in closed chain (46 +/- 43% MVC). Conclusions: Exercise in closed kinetic chain promotes more balanced initial quadriceps activation than does exercise in open kinetic chain. This may be of importance in designing training programs aimed toward control of the patellofemoral joint.

Digitally-implemented naturally sampled PWM suitable for multilevel converter control

For dynamic closed loop control of a multilevel converter with a low pulse number (ratio of switching frequency to synthesized fundamental), natural sampled pulse-width modulation (PWM) is the best form of modulation. Natural sampling does not introduce distortion or a delayed response to the modulating signal. However previous natural sampled PWM implementations have generally been analog. For a modular multilevel converter, a digital implementation has advantages of accuracy and flexibility. Re-sampled uniform PWM is a novel digital modulation technique which approaches the performance of natural PWM. Both hardware and software implementations for a five level multilevel converter phase are presented, demonstrating the improvement over uniform PWM.