Novel partitioned time integration methods for DAE systems based on L‐stable linearly implicit algorithms

Abstract

SUMMARYReal-time applications based on the principle of Dynamic Substructuring require integration methods that can deal with constraints without exceeding an a priori fixed number of steps. For these applications, first we introduce novel partitioned algorithms able to solve DAEs arising from transient structural dynamics. In particular, the spatial domain is partitioned into a set of disconnected subdomains and continuity conditions of acceleration at the interface are modeled using a dual Schur formulation. Interface equations along with subdomain equations lead to a system of DAEs for which both staggered and parallel procedures are developed. Moreover under the framework of projection methods, also a parallel partitioned method is conceived. The proposed partitioned algorithms enable a Rosenbrock-based linearly implicit LSRT2 method, to be strongly coupled with different time steps in each subdomain. Thus, user-defined algorithmic damping and subcycling strategies are allowed. Secondly, the paper presents the convergence analysis of the novel schemes for linear single-Degree-of-Freedom (DoF) systems. The algorithms are generally A-stable and preserve the accuracy order as the original monolithic method. Successively, these results are validated via simulations on single-and three-DoFs systems. Finally, the insight gained from previous analyses is confirmed by means of numerical experiments on a coupled spring-pendulum system.

An explicit time integration method for structural dynamics using septuple B-spline functions

“…One is explicit (see, e.g., [3][4][5][6][7][8]). The other is implicit (see, e.g., [9][10][11][12]). A method is explicit if the equation of motion of the current time step is not applied to determine the current displacement, while it is implicit if that is involved.…”