A theory of development and design of generalized integration operators for computational structural dynamics

A standardized formal theory of development/evolution, characterization and design of a wide variety of computational algorithms emanating from a gene ralized time weighted residual philosophy for dynamic analysis is first pre sented with subsequent emphasis on detailed formulations of a particular cl ass relevant to the so-called time integration approaches which belong to a much broader classification relevant to time discretized operators. Of fun damental importance in the present exposition is the evolution of the theor etical design and the subsequent characterization encompassing a wide varie ty of time discretized operators, and the proposed developments are new and significantly different from the way traditional modal type and a wide var iety of step-by-step time integration approaches with which we are mostly f amiliar have been developed and described in the research literature and in standard text books over the years. The theoretical ideas and basis toward s the evolution of a generalized methodology and formulations emanate under the umbrella and framework and are explained via a generalized time weight ed philosophy encompassing single-field and two-field forms of representati ons of the semi-discretized dynamic equations of motion. Therein, the devel opments first leading to integral operators in time, and the resulting cons equences then systematically leading to and explaining a wide variety of ge neralized time integration operators of which the family of single-step tim e integration operators and various widely recognized and new algorithms ar e subsets, the associated multi-step time integration operators and a class of finite element in time integration operators, and their relationships a re particularly addressed. The generalized formulations not only encompass and explain a wide variety of time discretized operators and the recovery o f various original methods of algorithmic development, but furthermore, nat urally inherit features for providing new avenues which have not been explo red and/or exploited to-date and permit time discretized operators to be un iquely characterized by algorithmic markers. The resulting and so-called di screte numerically assigned [DNA] markers not only serve as a prelude towar ds providing a standardized formal theory of development of time discretize d operators and forum for selecting and identifying time discretized operat ors, but also permit lucid communication when referring to various time dis cretized operators. That which constitutes characterization of time discret ized operators are the so-called DNA algorithmic markers which essentially comprise of both (i) the weighted time fields introduced for enacting the t ime discretization process, and (ii) the corresponding conditions these wei ghted time fields impose (dictate) upon the approximations (if any) for the dependent field variables in the theoretical development of time integrato rs and the associated updates of the time discretized operators. Furthermor e, a single analysis code which permits a variety of choices to the analyst is now feasible for performing structural dynamics computations on modern computing platforms. Copyright (C) 2001 John Wiley & Sons, Ltd.