Modified Iterative Group-Implicit Algorithm for the Dynamic Analysis of Structures

Abstract

In this work, the convergence characteristics of the iterative group-implicit (IGI) algorithm, which is a parallel algorithm for the time integration of the equations of motion arising in structural dynamics problems, are studied. It is found that the IGI algorithm does not always converge. For realistic structural applications, the time-step size must be limited to impractical values, which jeopardizes its efficiency, thus, defeating its purpose. The modified IGI (MIGI) algorithm is developed to address the convergence handicaps of the IGI algorithm. The new method incorporates new approaches in a number of areas, such as on the interface compatibility enforcement calculation, imbalance force distribution, and interface convergence checks. The convergence characteristics and limitations of the two algorithms are compared. It is found that the performance of the MIGI algorithm is far superior to that of the IGI algorithm. Through the numerical simulation of a practical structural engineering application, it is found that the MIGI algorithm is very efficient and produces highly accurate solutions.