A robust self‐starting explicit computational methodology for structural dynamic applications: Architecture and representations

Abstract

AbstractConventional 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 employing finite difference approximations for deriving the appropriate step‐by‐step algorithms. And, almost all of the widely advocated (existing) 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, in this paper we introduce new representations and architecture towards providing not only direct self‐starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time‐integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax–Wendroff‐type formulations. Therein, discretization in space is accomplished by introducing stress‐based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.