Papers by Keyword: Numerical Method

Abstract: The aim of this work is to analyze the error of the calculated integrated intensity of the x-ray peaks of a-iron (BCC-Fe) powder from x-ray diffraction (XRD) pattern by using the numerical method and the statistical analysis. The a-Fe powder was characterized by the x-ray diffractometer using step scan mode, step sizes 0.03^o 2q and 0.05^o 2q, and preset times from 0.1 to 3.5 s. The integrated intensity () of an x-ray peak and its error () were calculated using numerical method. The correlation between the relative error () and the preset time or step size were analyzed by the statistical analysis methods which are linear regression and statistical hypothesis testing. The results from the statistical analysis at significance level of 0.05 show that the relative error () correlate with x = preset time or integrated intensity by when a₁ and a₂ are the positive constants. From the mathematical model, for this work, the step size does not affect the relative error. However, the increasing of preset time reduces relative error on integrated intensity calculation. To minimize the error on XRD analysis, the preset time should be greater than one second. Moreover, on a XRD pattern, the lower integrated intensity peak has the higher relative error.

Abstract: A numerical method is proposed for calculating the fractional order derivative and successfully resolving the integrand singularity problem based on Zhang-Shimizu algorithm. And then a method is developed to calculate the twice nonlinear fractional derivative, numerical examples demonstrate the numerical method with high precision and good stability.

Abstract: The rolled homogeneous armour (RHA) plate is commonly used for armoured vehicle skin. Preliminary predictions of the deflections from RHA plate subjected to blast loading is important for establishing guidelines before it is used in vehicle skin. The goal of this work is a reliable technique for predicting the RHA plate response subjected to blast loading, and the empirical result performed by other researchers will be taken as a reference. Based on selected references, a small number of assumptions lead to the developed Single Degree of Freedom (SDOF) idealised models. This paper provides an analytical prediction for the RHA plate response using SDOF in one dimension (1D) approach. The analytical capability was subsequently verified using the non-linear fluid structure interaction (FSI) numerical simulation and the AUTODYN computer code. The midpoint deflections of the RHA plate were taken as the figure of merit. Based on the small error percentage and the support of strong analytical arguments, the second order SDOF analytical approach and numerical simulation using the AUTODYN computer code can be employed as a method of analysis.

Abstract: The investigation on mixed convection boundary layer of a viscoelastic fluid over a sphere which is embedded in porous medium under convective boundary condition is carried out in this paper. The boundary layer equations of viscoelastic fluid are an order higher than Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Hence, the augmentation on extra boundary conditions is needed in order to solve this problem. The governing partial differential equations are first transformed into non-dimensional forms and then solved numerically using the Keller-box method by augmenting extra boundary conditions at infinity. The numerical results obtained for limiting case are comparing with related outcomes in order to validate the present results. Results on the effects of the viscoelastic parameter in the presence of porosity and mixed convection on the skin friction and heat transfer as well as velocity and temperature profile have been discussed.

Abstract: Nonlinear dynamic behaviors of the fractional calculus model viscoelastic arch are discussed in this paper. The motion equations governing dynamic behaviors of the viscoelastic arch is derived and simplified by Galerkin method. The numerical method for solving the motion equations with fractional calculus is presented here. The influences of the load parameter and the material parameter are considered respectively. The results show that the chaotic vibration of the arch appears in forced vibration. And both the load parameter and the material parameter affect the dynamic behavior of the arch. With the increasing of the load parameter, the motion states changed from periodic motion with period 1 to complex motions, such as mult-periodicity, quasi-periodicity or chaos. The increasing of the material parameter benefits the stability of the structures.

Abstract: In the rapid new automobile development, the use of simulation technology is highly demanded due to shorter time to market and fashionable product styling that go beyond the rule-of-thumb in the manufacturing technology. In stamping simulation, the expected predictions rest with the part formability, spring back, blank optimization, and other vehicle integration works. These predictions are conducted concurrently during detailed product design, and intensive product validation is performed based on such predictions. In current work, it has established the experimental mechanical properties and flow curve data for thin galvanized sheet metal. Furthermore, the true prediction of part formability is investigated with established data and standard material database embedded in commercial simulation software. The tensile experiments were carried out on a uniaxial hydraulic tensile test machine with sheet metal specimen and in accordance to ASTM requirements. Three different sheet metal specimens were prepared from the longitudinal, transverse and 45⁰ degrees from the rolling direction. From experimental works and formulation, the mechanical properties, anisotropy and flow curve had been obtained. Further improvement in the embedded material database increases the prediction accuracy of FEM analysis for Body-in-White structure and crash performance.

Abstract: Based on the assumption of plane section, ideal elastic-plastic model of steel and the constitutive relations of concrete in Chinese Code for Design of Concrete Structures, numerical method is used to analyze the relationship of the axial force-moment-curvature on RC section. After dividing the normal section into strips, we adopt the secant stiffness iteration method (according to the results of each iteration, modify the secant stiffness through changing the elastic modulus of materials) to compile computer program. The results of the paper show a good agreement with those of the analytical method. Comparing with the analytical method, the numerical method of the paper can be wildly used in the application.

Abstract: In order to take advantage of the computer in the numerical calculation, in view of the fault tree qualitative analysis, a new method of fault tree analysis, numerical methods, was proposed on the basis of absorbing merits of the prime number method and determinant method. The fault tree's minimum cut sets and path sets can be calculated effectively with this method. Consequently, a specific example about calculation of the minimum cut sets was demonstrated with Scilab in this paper.

Abstract: This paper presents two dimensional fluid structure interaction (FSI) CFD analysis on the effect of skin thickness and Reynolds number on the aerodynamic performance of NACA 64₃-218 airfoil. Numerical investigations were performed using FLUENT 6.3 fluid flow solver and ABAQUS 6.8-1 structural solver. Coupling of both solvers in real time mode was accomplished with the Mesh based parallel Code Coupling Interface (MpCCI 3.1). The predicted and experimental results were found to be in excellent match. Generally, the results showed that the aerodynamic lift increases while drag decreases with the decrease of membrane thickness.

Abstract: Cable-stayed bridge is main kind of modern large-span bridges. Wind load and vehicle load are main dynamic force on cable stayed-bridge, which can cause large amplitude vibration of cables. In the paper, the nonlinear vibration differential equations of cable with dynamic displacement at its end point in 3D space was derived. The differential equations were analysed by the method of multiple scales and the vibration characteristic was discussed. The differential equations were solved by numerical method. The Trajectory of the cable middle point was plotted. The result of this paper indicated that the vibration amplitude of cable in 3D space is relate to the frequency and amplitude of the dynamic displacement of the cable end point. The results in the paper could be a reference for the research of cable vibration in cable-stayed bridge.