The subcycled Newmark algorithm
The Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different time steps in different regions of a structural model. The algorithm avoids numerical instabilities for a wide range of a one-to-two time step ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. The use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.
scientific article; zbMATH DE number 1058798