Application Analysis of an Improved N-R Iterative Method about Finite Element Numerical Calculation

Abstract

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.