A STUDY OF THE STABILITY OF SUBCYCLING ALGORITHMS IN STRUCTURAL DYNAMICS

Algorithms for explicit integration of structural dynamics problems wi th multiple time steps (subcycling) are investigated. Only one such al gorithm, due to Smolinski and Sleith has proved to be stable in a clas sical sense. A simplified version of this algorithm that retains its s tability is presented. However, as with the original version, it can b e shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are obse rved. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modif ied to give the subcycling algorithm. A related problem is shown to ar ise when a constraint equation in time is introduced into a time-conti nuous space-time finite element model. (C) 1998 Elsevier Science S.A.