Papers by Keyword: Newton-Raphson Iteration Method

Abstract: Based on positional FEM (finite element method), the nonlinear static formulation to treat large deflection of variable cross-section beam element is created by using the lowest potential energy theory. Adopting linear constitutive relation for hyper-elastic materials, the formulation and the solution procedure by Newton-Raphson iteration method are very simple.

Abstract: An algorithm is presented for maximum likelihood estimation (MLE) of three-parameter Weibull distribution in this paper, which is not only suitable for uncensored data but also appropriate for various censored data. Firstly, a unified likelihood equation under censored data and uncensored data was built. Here, the second-order convergent Newton-Raphson iteration method was applied to solve the MLE of two-parameter Weibull distribution, which had only scale parameter and shape parameter with a given positional parameter. Then, the steady and rapid Brent search method was applied to solve the optimal solution of the likelihood function just with a single variable of positional parameter. Finally, several examples were given to demonstrate the stability and efficiency of this algorithm.

Abstract: In this study, the digital image correlation method(with Newton-Raphson iteration method) is used to measure the in-plane deformation of poly-crystal aluminum. When the specimen is exerted a tensile load, the strain distribution of the specimen surface will be inhomogeneous. The micro-deformation of the poly-crystal aluminum is studied under a SEM(scanning electron microscope), a series of images of the micro crystal are captured during the loading process. By using digital image correlation to analyze the images, the displacement and strain of a micro-crystal are obtained, which provide important data for further analysis of the inhomogeneous properties of the poly-crystal aluminum.