Robust self-starting explicit computational methodology for structural dynamic applications: Lax-Wendroff/Taylor-Galerkin concept

Conventional approaches for computational structural dynamics (CSD) relevant to time-integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employ finite difference approximations for deriving the appropriate step-by-step algorithms. Almost all of the widely advocated step-by-step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, this paper proposes new developments and architecture towards providing a direct self-starting and robust methodology of computation for linear/nonlinear structural dynamics, in particular, the development of explicit time-integration formulations. Numerical test models are presented to validate the proposed developments.