The subcycled Newmark algorithm
type: Item
instance of: scholarly article
title: The subcycled Newmark algorithm
zbMATH Open document ID: 0898.73074
author: William J. T. Daniel
published in: Computational Mechanics
publication date: 1997-09-09T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1058798
zbMATH Keywords: numerical instabilities
zbMATH Keywords: nodal partition
zbMATH Keywords: different time steps
zbMATH Keywords: one-to-one time step ratio
zbMATH Keywords: unconditional stability
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: viscous damping
MaRDI profile type: Publication
full work available at URL: s004660050248
OpenAlex ID: W2069788614
DOI: 10.1007/S004660050248
description: scientific article; zbMATH DE number 1058798