Robust Convergence for the Dynamic Analysis of MDOF Elastoplastic Systems

Abstract

Direct time integration is the most popular method for solving nonlinear equations of motion. Because of the inherent error in most of these methods, in order to use the responses caused by analyses in design, it is customary to repeat them with smaller time steps. However, except for some complicated, new, and yet not practical time integration methods, this methodology does not always work in nonlinear regimes. To overcome this drawback, a methodology succeeded to cause robust convergence for dynamic analysis of single degree of freedom elastoplastic systems is suggested in this chapter. The main idea of the suggested methodology is to choose the nonlinearity detection tolerance so as to cause the truncation inherent error to have the most contribution in the total error. The chapter discusses a brief study of the non-convergence problem in nonlinear dynamic analysis. A generalized methodology is suggested for robust convergence of multiple degree of freedom elastoplastic systems. The efficiency of the suggested methodology is then studied using different numerical examples analyzed by different time integration methods. The numerical results reveal the considerable effect of this methodology on practical dynamic analysis.