The Effects of Newmark Method Parameters on Errors in Dynamic Extended Finite Element Method Using Response Surface Method

Abstract

The Newmark method is an effective method for numerical time integration in dynamic problems. The results of Newmark method are function of its parameters (β, γ and ∆t). In this paper, a stationary mode I dynamic crack problem is coded in extended finite element method )XFEM( framework in Matlab software and results are verified with analytical solution. This paper focuses on effects of main parameters in Newmark method for dynamic XFEM problems. Also use of the response surface method (RSM) a regression model is presented for estimating error of dynamic stress intensity factors (DSIF) with high validity according to results of analysis of variance (ANOVA). This work enables one to understand the effect of Newmark parameters on error of DSIFs and to find optimum β and γ for a determined number of time steps (N). This procedure is highly effective in order to  manage the computational cost and enhance the accuracy at the desired domain. The effect of the considered parameters on error, is investigated using RSM in Minitab software and optimum state for minimization of errors is illustrated.