ABSTRACT
A necessary condition for the uncondit ional stability of the algorithm for a non-linear system is that the operator 6K,:+i = K - Kl+i is positive semi-definite, where Ki+i is defined as the average stiffness matrix between the time steps iAt and (i + l)At (Pleslia and Belytschko (1985)). When the system is linearized and a £ [—1,0] .7 = "~~22"^ and ft = ^ ~i . the a-OS algorithm inherits both the unconditional stability and the low mode second-order accuracy of the o-uiethod (Hilber et al. (1977)). Like the a-method, it maintains favourable energy-dissipation properties in the higher part of the eigenfrequency spectrum.
