A parallel solution algorithm for nonlinear structural dynamics problems

In this research, a concurrent and domain-by-domain algorithm developed for the solution of transient analysis of structures, namely Iterative Group Implicit (IGI) algorithm (Modak 1997, Modak and Sotelino 2000), is investigated in detail and improved in terms of convergence and efficiency. It is found that in the IGI algorithm, the time step is severely limited due to stability constraints. The Modified Iterative Group Implicit (MIGI) algorithm is proposed as a solution to the convergence problem in the IGI algorithm. Direct averaging of the interface displacements, instead of the mass averaging, is found to be a better choice in the MIGI algorithm. The MIGI algorithm is shown to significantly speed-up the computations for linear structural dynamics problems along with a great accuracy. Generally, transient finite element analysis of real structures is computationally intensive, especially in the case of nonlinear analysis where frequent update/calculation of structural stiffness matrix is required. In this work, the MIGI algorithm is extended for the concurrent solution of nonlinear transient analysis of structures. In the proposed method the interface and interior convergence are achieved using separate iterative scheme. The convergence and effectiveness of the developed algorithm is studied through numerical studies. The MIGI algorithm is found to have an even better performance for the case of fully nonlinear transient analysis than it does for the linear case. The proposed MIGI algorithm should help in the simulation of the second-order inelastic transient analysis of large-scale structural systems in research and practice within a more reasonable analysis time