Multi‐time‐step domain coupling method with energy control

Abstract

AbstractA multi‐time‐step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state‐space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time‐integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state‐space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces. Copyright © 2010 John Wiley & Sons, Ltd.