STABILITY OF AN EXPLICIT MULTITIME STEP INTEGRATION ALGORITHM FOR LINEAR STRUCTURAL DYNAMICS EQUATIONS

A proof of stability is developed for an explicit multi-time step inte gration method of the second order differential equations which result from a semidiscretization of the equations of structural dynamics. Th e proof is applicable to an algorithm that partitions the mesh into su bdomains according to nodal groups which are updated with different ti me steps. The stability of the algorithm is demonstrated by showing th at the eigenvalues of the amplification matrices lie within the unit c ircle and that a pseudo-energy remains constant. Bounds on the stable lime steps for the nodal partitions are developed in terms of element frequencies.