The fundamentals underlying the computations of acceleration for general dynamic applications: Issues and noteworthy perspectives

To-date, with the exception of the Newmark method and the midpoint rule, most computational algorithms under the umbrella of LMS methods, which are predominantly employed in research and commercial software fail to properly evaluate acceleration computations accurately for conducting the numerical dynamic simulations. Indeed, this is not trivial and a sound theoretical basis of the fundamental underlying issues is described in detail. In this paper, we provide a resolution and point-out several noteworthy perspectives to address the proper evaluation of acceleration computations for structural dynamics applications with focus on the class of LMS methods as an illustration.