A variationally consistent framework for the design of integrator and updates of generalized single step representations for structural dynamics

A variationally consistent framework leading to the concise design of both the 'integrator' and the associated 'updates' as related to the single step representations encompassing the so-called LMS methods for structural dynamics is described. The present paper shows for the first time, a consistent treatment involving both the 'integrator' and 'updates' that are inherent in the general context of designing the time integration process. Furthermore, the framework encompasses not only all the existing time integration algorithms that are dissipative and non-dissipative within the scope of LMS methods but also contains new optimal algorithms useful for practical applications-in the sense of accuracy, stability, numerical dissipation and dispersion, and overshoot characteristics of computational algorithms for time dependent problems encountered in structural dynamics.