A generalization of the IDQ method and a DQ-based approach to approximate non-smooth solutions in structural analysis

In this paper, a new differential quadrature (DQ)-based approach in deducing the discretized equations governing the static and the dynamic problem of the Euler–Bernoulli beam is proposed. These equations, here called generalized, can be written easily, also thanks to a lemma, introduced for the first time, which allow a compact writing of the solution. By means of a careful distribution of the sampling points, the proposed method overcomes the drawback of the element subdivision where load conditions change. This is particularly useful in the analysis of some multi-degree-of-freedom dynamic systems, as it will be shown. The cited distribution and the way of generating it allow to generalize the iterative differential quadrature method, confined, in its initial form, to the two-degree-of-freedom systems.