A scalable TFETI algorithm for two-dimensional multibody contact problems with friction

A Total FETI (TFETI) based domain decomposition algorithm with preconditioning by a natural coarse grid of rigid body motions is adapted to the solution of two-dimensional multibody contact problems of elasticity with the Coulomb friction and proved to be scalable for the Tresca friction. The algorithm finds an approximate solution at the cost asymptotically proportional to the number of variables provided the ratio of the decomposition parameter and the discretization parameter is bounded. The analysis is based on the classical results by Farhat, Mandel, and Roux on scalability of FETI with a natural coarse grid for linear problems and on our development of optimal quadratic programming algorithms for bound and equality constrained problems. The algorithm preserves parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate a high efficiency of our algorithm. In addition, its performance is illustrated on analysis of the yielding clamp connection with the Coulomb friction.     

A new type of full multigrid method for the elasticity eigenvalue problem

This paper introduces a new type of full multigrid method for the elasticity eigenvalue problem. The main idea is to avoid solving large scale elasticity eigenvalue problem directly by transforming the solution of the elasticity eigenvalue problem into a series of solutions of linear boundary value problems defined on a multilevel finite element space sequence and some small scale elasticity eigenvalue problems defined on the coarsest correction space. The involved linear boundary value problems will be solved by performing some multigrid iterations. Besides, some efficient techniques such as parallel computing and adaptive mesh refinement can also be absorbed in our algorithm. The efficiency and validity of the multigrid methods are verified by several numerical experiments.     

A new Bernoulli–Euler beam model incorporating microstructure and surface energy effects

A new Bernoulli–Euler beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equation and complete boundary conditions for a Bernoulli–Euler beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface elasticity constants describing the mechanical behavior of the beam surface layer. The inclusion of these additional material constants enables the new model to capture the microstructure- and surface energy-dependent size effect. In addition, Poisson’s effect is incorporated in the current model, unlike existing beam models. The new beam model includes the models considering only the microstructure dependence or the surface energy effect as special cases. The current model reduces to the classical Bernoulli–Euler beam model when the microstructure dependence, surface energy, and Poisson’s effect are all suppressed. To demonstrate the new model, a cantilever beam problem is solved by directly applying the general formulas derived. Numerical results reveal that the beam deflection predicted by the new model is smaller than that by the classical beam model. Also, it is found that the difference between the deflections predicted by the two models is very significant when the beam thickness is small but is diminishing with the increase of the beam thickness.     

基于门限面板模型的我国能源利用效率研究

根据三要素的柯布-道格拉斯生产函数,构建我国能源利用效率的门限面板模型,对2000~2014年我国30个省份(不含西藏)的样本数据,进行实证分析.研究表明:能源利用效率变量存在明显的三门限值,把我国30个省份分成四大类,不同类别的地区在能源效率和能源投入规模上存在显著差异.能源利用效率比较高的地区能源利用效率随能源投入增加而变大,而能源利用效率较低地区则相反.另外能源利用效率高的地区,能源投入规模大,能源产出弹性也大,说明在一定程度上对经济的贡献率也比较大,且未来继续靠能源拉动经济的可能性也比较大.     

Solutions of half-space and half-plane contact problems based on surface elasticity

Analytical solutions for the problems of an elastic half-space and an elastic half-plane subjected to a distributed normal force are derived in a unified manner using the general form of the linearized surface elasticity theory of Gurtin and Murdoch. The Papkovitch–Neuber potential functions, Fourier transforms and Bessel functions are utilized in the formulation. The newly obtained solutions are general and reduce to the solutions for the half-space and half-plane contact problems based on classical linear elasticity when the surface effects are not considered. Also, existing solutions for the half-space and half-plane contact problems based on simplified versions of Gurtin and Murdoch’s surface elasticity theory are recovered as special cases of the current solutions. By applying the new solutions directly, Boussinesq’s flat-ended punch problem, Hertz’s spherical punch problem and a conical punch problem are solved, which lead to depth-dependent hardness formulas different from those based on classical elasticity. The numerical results reveal that smoother elastic fields and smaller displacements are predicted by the current solutions than those given by the classical elasticity-based solutions. Also, it is shown that the out-of-plane displacement and stress components strongly depend on the residual surface stress. In addition, it is found that the new solutions based on the surface elasticity theory predict larger values of the indentation hardness than the solutions based on classical elasticity.     

应用随机前沿成本模型对我国大型综合医院成本效率的研究

为了精确考察我国大型医院医疗服务和管理的成本效率,采用随机前沿成本模型对我国73所大型综合医院的医疗服务的成本效率进行了评价研究,同时在3种不同低效率误差分布的假设下,对各评价单元所得的效率值进行了比较.结果显示,我国大型综合医院医疗服务的成本效率平均得分在0.9以上,表明它们的医疗服务和管理水平是比较高的,与其发展规模是相匹配的.并且在3种不同的低效率误差分布假设下各评价单元所得效率值也基本一致.     

基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。     

Bag rationalisation for a food manufacturer

A food manufacturer has decided to rationalise the types of bags used to pack their products with a view to achieving economies of scale and improved efficiency. Under the new regime, the name and characteristics of the product are to be printed on the bag during packaging, with the bag colour as a secondary distinctive feature. There are several ways of describing the director's conflicting objectives of minimising both cost and customer colour conflicts. We model the problem in two ways: as a Zero-One Integer Programme, and as a variant of a classical Graph Colouring Problem. Problem-specific observations, and data pre-processing, enable us to decompose the originally intractable problem, and to solve it using commercial integer programming software. Our solution compares favourably with that from a heuristic for graph colouring and our recommended allocation of eight colours was accepted for implementation.     

A posteriori error estimation for the dual mixed finite element method of the elasticity problem in a polygonal domain

In this article, we propose a residual based reliable and efficient error estimator for the new dual mixed finite element method of the elasticity problem in a polygonal domain, introduced by M. Farhloul and M. Fortin. With the help of a specific generalized Helmholtz decomposition of the error on the strain tensor and the classical decomposition of the error on the gradient of the displacements, we show that our global error estimator is reliable. Efficiency of our estimator follows by using classical inverse estimates. The lower and upper error bounds obtained are uniform with respect to the Lamé coefficient λ, in particular avoiding locking phenomena. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.     

A comment on “cost efficiency in data envelopment analysis with data uncertainty”

In a recent paper by Mostafaee and Saljooghi [Mostafaee, A., Saljooghi, F.H., 2010. Cost efficiency in data envelopment analysis with data uncertainty. European Journal of Operational Research, 202, 595–603], the authors extend the classical cost efficiency model to address data uncertainty. They claim that the upper bound of the cost efficiency can be obtained at extreme points when the input prices appear in the form of ranges. In this paper, we present our counterexamples and comments on the contention by Mostafaee and Saljooghi.     

Vibration analysis of Nano-Rotor's Blade applying Eringen nonlocal elasticity and generalized differential quadrature method

This study investigates the small scale effect on the flapwise bending vibrations of a rotating nanoplate. The nanoplate is modeled with a classical plate theory and considering cantilever and propped cantilever boundary conditions. Due to the rotation, the axial forces are included in the model as true spatial variation. Hamilton's principle is used to derive the governing equation and boundary conditions of the classical plate theory based on Eringen's nonlocal elasticity theory. The generalized differential quadrature method is employed to solve the governing equation. The effect of small-scale parameter, non-dimensional angular velocity, non-dimensional hub radius, aspect ratio, and different boundary conditions in the first four non-dimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nano-machines such as nano-motors and nano-turbines and other nanostructures.     

Reduced warp in torsion of reticulated foam due to Cosserat elasticity: experiment

Warp of cross sections of square section bars in torsion is reduced in Cosserat elasticity in comparison with classical elasticity. Warp is observed experimentally to be substantially reduced, by about a factor of four compared with classical elasticity, in an open-cell polymer foam for which Cosserat elastic constants were previously determined. The observed warp in the foam is consistent with a prediction based on Cosserat elasticity. Concentration of strain in the foam is therefore reduced in comparison with classical elasticity.     

A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation

In this paper we focus on scale elasticity measure based on directional distance function for multi-output–multi-input technologies, explore its fundamental properties and show its equivalence with the input oriented and output oriented scale elasticity measures. We also establish duality relationship between the scale elasticity measure based on the directional distance function with scale elasticity measure based on the profit function. Finally, we discuss the estimation issues of the scale elasticity based on the directional distance function via the DEA estimator.     

Parallel preconditioners for large scale partial difference equation systems

We propose a new preconditioner DASP (discrete approximate spectral preconditioner), based on the existing well-known preconditioners and our computational experience. Parallel preconditioning strategies for large scale partial difference equation systems arising from partial differential equations are investigated. Numerical results are given to show the efficiency and effectiveness of the new preconditioners for both model problems and real applications in petroleum reservoir simulation.     

Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory

A gradient-enriched shell formulation is introduced in the present study based on the first order shear deformation shell model and the stress gradient and strain-inertia gradient elasticity theories are used for dynamic analysis of single walled carbon nanotubes. It provides extensions of the first order shear deformation shell formulation with additional higher-order spatial derivatives of strains and stresses. The higher-order terms are introduced in the formulation by using the Laplacian of the corresponding lower-order terms. The proposed shell formulation includes two length scale size parameters related to the strain gradients and inertia gradients. The effects of the transverse shear, aspect ratio, circumferential and half-axial wave numbers and length scale parameters on different vibration modes of the single-walled carbon nanotubes are elucidated. The results are also compared with those obtained from a classical shell theory with Sanders–Koiter strain-displacement relationships.     

Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails

We consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction as well as the efficiency gain of our method over another fast standard technique based on the classical Pollaczek-Khinchine formula. We provide a numerical example to illustrate the performance, and show that for more time-consuming conditional Monte Carlo techniques, the new series representation also does not compare unfavorably to the one based on the Pollaczek-Khinchine formula.

     

Refined geometrically nonlinear equations of motion for elongated rod-type plate

We derive new refined geometrically nonlinear equations of motion for elongated rod-type plates. They are based on the proposed earlier relationships of geometrically nonlinear theory of elasticity in the case of small deformations and refined S. P. Timoshenko’s shear model. These equations allow to describe the high-frequency torsional oscillation of elongated rod-type plate formed in them when plate performs low-frequency flexural vibrations. By limit transition to the classical model of rod theory we carry out transformation of derived equations to simplified system of equations of lower degree.     

Consistency of returns-to-scale characterizations of production frontiers with respect to model specification

Returns-to-scale (RTS) characterizations and the underlying notion of scale elasticity are important characteristics of production frontiers, in both parametric and nonparametric methodologies of efficiency and productivity analysis. In practical applications of these methodologies, the model of technology is often experimented with and modified before it is finalized, which involves, for example, a change of the data set, incorporation, exclusion or aggregation of inputs and outputs, or experimentation with the production assumptions, or axioms, on which the model is based. While it is well-known how such modifications of technology affect the efficiency scores, their effect on the RTS characterization of the production frontier has not been sufficiently explored in the literature. In this paper we obtain several general results that clarify this issue.     

Effects of a small length scale on vibrations of an embedded double-walled carbon nanotube

Extensive continuum analyses are carried out to estimate the influence of matrix stiffness, a small length scale, and intertubular radial displacements on free vibrations of an individual double-walled carbon nanotybe. The analyses are based on both local and classical Euler–Bernoulli and Timoshenko elasticity theories with concentricity and nonconcentricity assumptions. The effect of a small length scale is incorporated in the formulations. New intertubular resonant frequencies are calculated based on these theories. Detailed results are demonstrated for the resonant frequencies as functions of matrix stiffness and the small length scale. The results indicate that the internal radial displacement and the stiffness of the surrounding matrix can greatly affect the resonant frequencies, especially at higher frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. More over, at high frequencies and small aspect ratios, the effect of the small length scale be comes more significant.