Ein lösbarkeitskriterium für ein mehrstufen – mehrsorten – transportproblem

A variant for checking a solvability eriterion for multilevel multisort transportation problem is given.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

The LS1 model for delamination propagation in multilayered materials at 0°/θ° interfaces: A comparison between experimental and finite elements strain energy release rates

The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only depends on the stacking sequence and the position of delamination is presented.     

On the Bullwhip Avoidance Phase: The Synchronised Supply Chain

The aim of this paper is to analyse the operational response of a Synchronised Supply Chain (SSC). To do so, first a new mathematical model of a SSC is presented. An exhaustive Latin Square design of experiments is adopted in order to perform a boundary variation analysis of the main three parameters of the periodic review smoothing (S, R) order-up-to policy: i.e., lead time, demand smoothing forecasting factor, and proportional controller of the replenishment rule. The model is then evaluated under a variety of performance measures based on internal process benefits and customer benefits. The main results of the analysis are: (I) SSC responds to violent changes in demand by resolving bullwhip effect and by creating stability in inventories under different parameter settings and (II) in a SSC, long production–distribution lead times could significantly affect customer service level. Both results have important consequences for the design and operation of supply chains.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

On the determination of the point of fracture initiation by the load separation criterion in J-testing of ductile polymers

The application of an experimental approach based on the load separation criterion for the determination of the point of fracture initiation in a fracture test on a ductile polymer was critically examined. To this aim, the fracture process outlined by the application of this method was related to that described by the visual analysis of the fracture surfaces obtained in fracture tests on nominally identical specimens, in which different levels of crack extension were produced. The material examined was an acrylonitrile-butadiene-styrene (ABS) resin, and the fracture tests were performed at low loading rate on single-edge notched in bending specimens.The results demonstrated that this load separation criterion based methodology is a promising approach for the determination of the point of fracture initiation, and for material fracture resistance, J_Ic, evaluation. The method also has experimental simplicity and a high degree of repeatability.     

氢键准则在DMSO水溶液中应用的评价

利用分子动力学模拟方法, 分别采用几何准则和能量准则分析了不同浓度下的二甲基亚砜(DMSO)水溶液的氢键统计和动力学等特性. 结果显示, 两种氢键准则可以很好地反映出溶液的氢键性质随浓度的变化趋势. 通过分析比较发现, 由于几何准则不能有效地排除具有弱对势能的分子对, 因此其统计的氢键数量要大于能量准则的结果.此外, 能量准则对于分子间相对取向的区分存在不足, 进而引起氢键寿命的计算结果偏大.因此,为使氢键分析更加准确, 本文建议使用几何-能量混合型氢键准则.     

Discrete element simulation of effects of multicontact loading on single particle crushing

Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties. Unlike idealized particles in experimental single particle crushing tests with two loading points, natural particles are crushed under multicontact loading. To date, the criteria and patterns of particle crushing under multicontact conditions are not fully understood. By using the three-dimensional discrete element method, this report explores the effect of multicontact loading on the crushing criterion of a single particle, the crushing pattern, and the relationship between the particle crushing strength and loading distribution. The particles are modelled as aggregates of glued Voronoi polyhedra. The numerical results indicate that the logarithm of the mean principal stress has a good linear correlation with the coordination number. For a specific coordination number, the number of child particles presents a significant normal distribution. For a specific number of child particles, the volumes of child particles can be statistically described as normal or gamma distribution. Three typical models are proposed to qualitatively analyse the relationship between the loading distribution and crushing strength. The relevant conclusions can be helpful in engineering practice and in further studies on crushable granular materials via the discrete element method.     

A logarithmic regularity criterion for the 3D generalized MHD system

We prove a logarithmic regularity criterion for the 3D generalized magnetohydrodynamics (MHD) system with diffusion terms ?Δu and (?Δ)^βb, with . Copyright © 2015 John Wiley & Sons, Ltd.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015