Analysis of the neutral layer offset of bimetal composite plate in the straightening process using boundary element subfield method

In the classical straightening theory, it supposes that the geometric central layer and stress neutral layer are a coincidence. However, there is some offset in fact. This is one of the reasons why straightening force is inaccurate in the straightening process. In this paper, the boundary element subfield method is used to analyze the three-dimension elastic–plastic deformation of a bimetal composite plate in the straightening process. At first, the boundary integral equation of a bimetal composite plate is established by the boundary element subfield method. Then, through analyzing the deformation in the rolled piece straightening, it shows that the geometric central layer does not coincide with the neutral layer. The formula of the neutral layer offset is established and the change law is discussed. At the same time, the influence of the neutral layer offset on the precision of straightening force is researched. From the numerical analysis, it shows that the error of the straightening force reaches to 5% whether considering the neutral layer offset. This demonstrates that the neutral layer offset is one of the important factors to give the straightening force inaccurately. It is ought to consider the neutral layer offset when the model of straightening force is established.     

Stochastic models for the plastic rotation process in heat straightening of damaged steel plates

Two separate theoretical models are developed to predict the number of heat applications necessary to repair specified bends in damaged steel plates. One model is an application of the theory of reliability; this idealization is subsequently further simplified for practical engineering applications. The second is an application of the theory of stochastic processes: envisioning the record of plastic rotations obtained from the actual heat-straightening of a subject plate as a finite portion of a member of the infinite ensemble of possible records for the repair, and assuming this process to be stationary and ergodic in the heat-number domain, the theory of discrete spectral analysis is used to construct the power spectral density function of the process, and simulate artificial records. Then, simple statistical analysis allows the prediction with any desired degree of confidence. These independent probability-based estimates successfully verify each other. As expected, the required number of repair heats for each test in the ensuing experimental program, under carefully controlled laboratory conditions, was consistently smaller than the corresponding theoretical prediction.     

A finite element model for the fire-performance of GRP panels including variable thermal properties

A finite element study is conducted to determine the thermal response of a widely used glass reinforced plastic panel exposed to fire. This study is performed based on a formulation developed previously by the authors and improved by including the moisture and temperature-dependent thermal properties and a newly developed time-dependent non-linear mixed boundary condition at the unexposed surface of the panel. In addition, the influence of non-zero final resin mass is considered according to a recently performed thermal gravimetric analysis. In order to derive the appropriate element equations, a mixed explicit–implicit Bubnov–Galerkin finite element approach is adopted. Results of this study are presented for a standard, 10.9 mm, thickness of single-skinned polyester-based glass reinforced plastic panel and comprise temperature profiles, density distributions and moisture profiles. Comparisons are made between the predicted results and those obtained experimentally. The predicted temperatures agreed with the experimental results with an average difference of 21.41°C. A simple comparison of the present value with that of the authors’ previous model, 29.66°C, indicates a considerable improvement of 38.53% in the fire-performance prediction of the material.     

A penalty method for nonparametric estimation of the intensity function of a counting process

Nonparametric estimators are proposed for the logarithm of the intensity function of some univariate counting processes. An Aalen multiplicative intensity model is specified for our counting process and the estimators are derived by a penalized maximum likelihood method similar to the method introduced by Silverman for probability density estimation. Asymptotic properties of the estimators, such as uniform consistency and normality, are investigated and some illustrative examples from survival theory are analyzed.This work was conducted while the author was visiting the Department of Mathematics, University of California at Irvine.     

A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process

A generalization of the Cramér-Lundberg risk model perturbed by a diffusion is proposed. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at a constant rate with additional random fluctuation. The insurer is allowed to invest the surplus into a risky asset with volatility dependent on the level of the investment, which permits the incorporation of rational investment strategies as proposed by Berk and Green (2004). The return on investment is modulated by a Markov process which generalizes previously studied settings for the evolution of the interest rate in time. The Gerber-Shiu expected penalty-reward function is studied in this context, including ruin probabilities (a first-passage problem) as a special case. The second order integro-differential system of equations that characterizes the function of interest is obtained. As a closed-form solution does not exist, a numerical procedure based on the Chebyshev polynomial approximation through a collocation method is proposed. Finally, some examples illustrating the procedure are presented.     

Accurate stress analysis of sandwich panels by the differential quadrature method

Sandwich structures are widely used in many engineering fields. It is possible but not easy for an engineering theory to recover all stresses accurately. In this paper, a modeling strategy is proposed to simplify the formulation. A classical sandwich panel is firstly divided into three parts, equations of the top and bottom face sheets are used as the boundary conditions of the two-dimensional core and then only the core needs to be analyzed by the differential quadrature method (DQM). In this way, both displacement and stress can be accurately obtained. Detailed formulations are worked out. Three boundary conditions and three types of loading, including the concentrated load regarded as a challenging problem for point discrete methods such as the DQM, are considered to investigate the effect of boundary conditions and loading on the distributions of displacement and stress. For verification, results are compared with theoretical solutions or/and numerical data. Presented data may be a reference for other investigators to develop more accurate engineering beam theory or new numerical method.     

Combined Hermite spectral-finite difference method for the Fokker-Planck equation

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and is shown to improve the accuracy and effectiveness of the Hermite spectral approximation, with no increase in workload. Some basic analysis for the selection of the scaling factors is also presented.

     

Solution of non-linear thermal transient problems by a new adaptive time-step method in quenching process

Quenching process is a thermo-elastic-plasticity problem with a high material non-linearity. The numerical oscillation is likely caused in the simulation of quenching process. In order to avoid the numerical oscillation and improve the calculation accuracy of temperature and phase-transformation fields in the quenching process, a new self-adaptive time-step size method is presented. The method can adjust the time-step size according to the maximum and minimum differences of temperature fields between the previous simulation step and the current simulation step. FEM software for evaluating the temperature, stress/strain and phase-transformation is also developed. A cooling example with numerical analytical results and a quenching example with experiment results are used to verify the calculation accuracy of this software. Five methods including the method in this paper, two constant time-step sizes and two geometric proportion time-step sizes are applied to simulate the quenching process of a 40Cr steel cylinder, respectively. A comparison of the simulation results shows that, the method presented in this paper can effectively avoid the numerical oscillation, ensure the calculation accuracy and cost less calculation time.     

A method for minimizing the sum of a convex function and a continuously differentiable function

This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points.     

A minimization method for the sum of a convex function and a continuously differentiable function

This paper presents a method for finding the minimum for a class of nonconvex and nondifferentiable functions consisting of the sum of a convex function and a continuously differentiable function. The algorithm is a descent method which generates successive search directions by solving successive convex subproblems. The algorithm is shown to converge to a critical point.The authors wish to express their appreciation to the referees for their careful review and helpful comments.     

Multidomain spectral method for the Gauss hypergeometric function

Numerical Algorithms - Differentiation matrices are in wide use in numerical algorithms, although usually studied in an ad hoc manner. We collect here in this review paper elementary properties of...     

Relaxation method for constrained minimization of the maximum function

Translated from Issledovaniya po Prikladnoi Matematike, Kazan', No. 14, pp. 25–34, 1987.     

Confidence regions for the intensity function of a cyclic Poisson process

A classical approach to constructing simultaneous confidence intervals (i.e., confidence bands or regions) for a function is via establishing a limiting process of the appropriately normalized difference between the function and its empirical estimator. In the present paper we depart from this approach and construct confidence bands for the intensity function of a cyclic Poisson process via extreme value type asymptotic results for the appropriately normalized supremum of the difference between the intensity function and its empirical estimator.      

Combined use of the finite element and finite superelement methods

Results of the theoretical and numerical studies of an algorithm based on the combined use of the finite element and finite superelement methods are presented. Estimates of the errors for one of the variants of the method applied to solving the Laplace equation are obtained. The method can be used to solve a problem concerning the skin layer appearing due to high velocities.     

Vendor rating for an entrepreneur development programme: a case study using the analytic hierarchy process method

With collaborative purchasing programmes where one of the aims is to develop suppliers, vendor rating is important not only in supplier selection and in deciding how to allocate business but also to determine where scarce development effort is best applied. This paper describes a case study into vendor rating for a government sponsored Entrepreneur Development programme in Malaysia. The paper reviews current methods for vendor rating and finds them wanting. It illustrates a new approach based on the use of Saaty's Analytic Hierarchy process method, which was developed to assist in multi-criteria decision problems. The new method overcomes the difficulties associated with the categorical and simple linear weighted average criteria ranking methods. It provides a more systematic way of deriving the weights to be used and for scoring the performance of vendors.     

The variance function of the Erlang process

Summary A relatively simple exact expression of closed form is obtained for the varianceσ ²(t) of the asynchronous counting distribution for a counting period of lengtht,t>0, in an Erlang process. Useful bounds are placed upon the error of the linear approximation toσ ²(t). Implications of these results are examined. In particular, a new exact expression and related bounds are obtained for the mean function of the synchronous counts (also known as the renewal function of the process). All bounds given are sharp in asymptotic order of magnitude as the length of the counting period is allowed to increase. Prepared under Contract No. FH-11-6890, Bureau of Public Roads, Federal Highway Administration, U.S. Department of Transportation. The opinions, findings and conclusions expressed herein are those of the author and not necessarily those of the Bureau of Public Roads.