During the numerical calculation by FE (Finite Element) method, N-R (Newton-Raphson) iterative method will be used to solve the problem such that material performing with elasto-plastic character and geometric non-linearity. However, if the problem has macro scale DOFs (degree of freedom), the classical N-R method is shown to make a low efficiency on the whole process. For this reason, in this paper, an improved N-R iterative method is proposed by creating proper mandatory limiters to change the step size of displacement field increment. In this way, the size of single iterative step is enlarged in the new method with tangent stiffness matrix used as classical N-R iterative theory as well. Furthermore, to test stability of the new method, two models of structure are chosen to be calculated with this method. In the conclusion, the improved N-R iterative method is indicated to be an efficient and stable numerical method which could solve nonlinear problems, especially with macro scale DOFs.
Based on free-knot splines techniques, we develop a fully Bayesian method to make inference about the autoregressive and functional-coefficient moving-average models, including estimation and prediction. We approximate different functional-coefficients by polynomial splines with different orders to adapt to different smoothness. To make the estimation and prediction robust, we assign heavy-tailed student-t priors on the coefficients of both the splines and the autoregressive terms. The posterior predictive distribution is derived from a Bayesian model average over all of the possible models. The proposed method is demonstrated by both simulated and real data examples.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.