A new family of explicit generalized single-step single-stage integration methods for structural/multibody dynamics with improved stability for viscous damping

This article details the analysis and synthesis of a novel family of explicit single-step integration methods for the second-order dynamics of structural and multibody systems. The family is derived from the Generalized Single-Step Single-Solve framework, pertaining to the class of linear multistep methods. The new explicit methods achieve second-order accuracy with optimal starting error, controllable numerical dissipation, and an option for explicit or implicit treatment of damping; the latter yields a stability limit which scales optimally with modal damping ratio, unlike prior methods with only incidental gains. The new family is compared with existing explicit methods on the basis of numerical accuracy and stability. Its superior performance for linear and nonlinear systems is demonstrated by numerical examples.