颜色读数与物质浓度关系的数学建模

比色法作为一种检测物质浓度的常用方法,是通过待测物质溶液颜色读数来推测所含物质浓度,根据所提供的物质浓度与不同色卡颜色读数的试验数据,对物质浓度和颜色读数进行相关性分析,拟合颜色读数与物质浓度的指数模型和建立灰色预测模型,对这两种模型的拟合值与原始值的误差进行比较分析,给出了颜色读数与物质浓度关系的优化模型.     

基于特征正交分解的材料微结构参数化表征模型及等效性能优化设计

随着计算能力的不断发展,近年来基于材料微结构图像的材料等效性能数值模拟越来越受到学者们的重视.在此背景下,提出了一种针对材料微结构图像的高效参数化表征模型.通过特征正交分解(proper orthogonal decomposition,POD)对已有材料微结构图像数据进行特征分析,得到近似描述该类材料微结构的特征缩减基.应用移动最小二乘(moving least squares,MLS)法建立特征缩减基映射系数的响应面模型,拟合得到任意给定参量相应的缩减基映射系数.利用拟合缩减基系数可获得任意给定参量对应的微结构图像矩阵.该参数化表征模型被用于表征含椭球夹杂的两相材料(2-phase composite)的二维情形, 并进一步应用于这类复合材料宏观等效力学性能的优化设计.     

基于变体积约束的阻尼材料微结构拓扑优化研究北大核心CSCD

阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Applications of mathematical programming models

A sizeable proportion of manufacturing expenses can be attributed to facility layout and material handling. Facility layout decisions involve designing the arrangement of elements in manufacturing systems. Among the most critical material handling decisions in this area are the arrangement and design of material flow patterns. This survey article reviews loop based facility planning and material handling decisions for trip based material handling equipment with an emphasis on unit load automated guided vehicles. The article examines issues related with facility design, material handling design, and fleet sizing and operating.     

The strain-rate-dependent material and failure behaviour of 2D and 3D non-crimp glass-fibre-reinforced composites

For a reliable structural design of security-relevant, high-dynamically loaded light weight structures, the knowledge of the strain-rate-dependent material and damage behaviour, material properties, and validated material models have to be provided. For this purpose, various material tests at different strain rates have been performed on composites with a novel 3D-reinforced glass-fibre multilayered flat-bed weft-knitted fabric reinforcement by using a servohydraulic high-speed testing unit in combination with specially adapted clamping de vices. The highly dynamic material tests served to develop adequate material models in the classical sense of continuum damage mechanics and to determine the associated model parameters.     

用张量导数法求横观各向同性弹性材料的弹性张量的一般形式

用对张量函数求导的方法导出了横观各向同性材料和各向同性材料的弹性张量的一般形式与应力-应变关系式.从推导过程可更清楚地看出为什么横观各向同性材料和各向同性材料分别有五个和两个独立的弹性常数,即材料有几个独立的弹性常数是由其应变能函数的形式所决定的.     

基于合作博弈的预付条件下应急物资库存策略

应急物资储备是应急管理的主要工作之一.以往政府自己组织物资储备,不仅耗费大量人力、物力,且由于应急物资具有有效期等缘故,报废损失较大.本文考虑政府与供应商合作进行应急物资的实物储备,讨论在政府提前支付部分货款、供应商储备应急物资的库存策略,并从合作博弈的角度,确立了联盟的合作期限与政府提前支付货款比例,实现了在减少政府支出的前提下,动态存储定量应急物资,大幅度延长有效期的目标.最后使用算例验证了该策略的有效性.     

Remarks on the paper ‘Exact bounds on average granular pressures in a general bin model’

In the paper referred to in the title to this communication, Shahinpoor argued that increased density due to material consolidation of a bulk material in a vertical bin reduces the stresses the bulk material exerts on the bin wall below those that would be present if the material were unconsolidated. In this paper it is shown that increased density due to material consolidation actually increases rather than reduces these stresses. Shahinpoor's conclusions are incorrect because he misinterprets his analytical results.     

基于NSGA-II的应急生产任务多目标优化模型及算法研究

重大突发事件发生后,若灾区的应急物资需求不能通过调用储备得到满足,则应急生产将成为灾区应急物资供应的重要保障手段。本文研究重大突发事件发生后应急物资生产任务的优化问题,重点关注原材料生产能力变化对完成应急生产任务的影响,以应急生产任务完成时间最短、完成成本最低为决策目标,研究了包含多个供应商、多个制造商以及单个受灾点的应急物资生产任务多目标规划模型。运用在求解多目标规划问题时具有众多优势的非支配排序多目标遗传算法(NSGA-II)对模型进行求解。通过算例分析,NSGA-II可以得到较好的Pareto前沿,并且可以根据不同情况给出最优的应急物资生产和原材料保障方案。本文的研究还表明,要想更快完成应急生产任务,需要做好原材料、资金、电力、交通等各种要素的配套保障工作。     

大型水电工程物资调运建模及算法

根据小湾水电工程物资供应管理的实际情况,提出了物资调运的三级节点概念模型,论述了物资采购与调运的数学模型,并给出了具体算法。模型已应用于该工程物资调运决策支持系统中,运行实践表明,该模型能够辅助调度人员制定合理的物资采购与调运方案。     

Tension variations in pliable material in production machinery

A mathematical model of a high-speed material handling machine has been developed so that the variation of tension in the material can be predicted. The machine components can include free rollers, driven rollers and material rolls. The effects of friction between material and guide rollers have been included. Experimental work has been carried out to test the predictions of the model.     

突发事件情景下串联式需求系统应急物资协同调度研究

针对突发事件情景下串联式需求系统遭受破坏问题,分析了突发事件情景下串联式需求系统应急物资协同调度的特征。在对系统提供应急物资进行修复的基础上,以串联式需求系统修复的时间最短及成本最小为目标,分别构建了纵向配送的应急物资调度模型和纵向配送与横向转运相结合的应急物资协同调度模型,并设计一种遗传算法对两种模型进行求解。最后通过算例分析,求解得到两种模式下串联式需求系统应急物资调度的最优配送方案,比较解的结果,得出纵向配送与横向转运相结合的应急物资协同调度模式优于一般的应急物资纵向配送模式的结论,验证了该应急物资协同调度模式的有效性和可行性。     

Orientational Design of Nonorthotropic Two-Dimensional Materials

A linear elastic nonorthotropic two-dimensional material with six independent elastic parameters is considered. Different criteria for comparison of constitutive matrices, which may be mutually rotated, are discussed. Optimal material orientations of a nonorthotropic material, which correspond to extreme values of the energy density, are determined. The results obtained are extended to some nonlinear elastic material models.     

Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Material stability analysis of particle methods

Material instabilities are precursors to phenomena such as shear bands and fracture. Therefore, numerical methods that are intended for failure simulation need to reproduce the onset of material instabilities with reasonable fidelity. Here the effectiveness of particle discretizations in reproducing of the onset of material instabilities is analyzed in two dimensions. For this purpose, a simplified hyperelastic law and a Blatz–Ko material are used. It is shown that the Eulerian kernels used in smooth particle hydrodynamics severely distort the domain of material stability, so that material instabilities can occur in stress states that should be stable. In particular, for the uniaxial case, material instabilities occur at much lower stresses, which is often called the tensile instability. On the other hand, for Lagrangian kernels, the domain of material stability is reproduced very well. We also show that particle methods without stress points exhibit instabilities due to rank deficiency of the discrete equations. AMS subject classification 74S30     

一种装备维修器材保障准确性计算方法研究

装备维修器材保障准确性是影响装备维修保障工作的重要因素之一.从装备维修器材保障过程中所需满足的数量和品种入手,给出了一种装备维修器材保障准确性计算方法,最后提出了提高装备维修器材保障准确性的对策与措施.     

Managing raw material in supply chains

In this paper, we explore how firms can manage their raw material sourcing better by developing appropriate sourcing relationships with their raw material suppliers. We detail three empirical case studies of firms explaining their different raw material sourcing strategies: (a) firms can adopt a hands-off approach to raw material management, (b) firms can supply raw material directly to their suppliers, and this may be beneficial for some agents in the supply chain, and (c) firms can bring their component suppliers together, and the resulting cooperation between suppliers can be beneficial for supply chain. We then analytically model the three raw material scenarios encountered in our empirical work, examine the resulting profits along the supply chain, and extend the results to a competitive buyer scenario. Overall, our results show that active management of raw material sourcing can add value to supply chains.     

Analysis of a stress singularity in a non-linear Flamant problem for certain models of a material

A generalized plane problem in the non-linear theory of elasticity is considered for a half-plane loaded on the boundary with a concentrated external force (the non-linear Flamant problem). The properties of the material of the half-plane are described by different (known) models, and each model of the non-linearly elastic material generates its own specific boundary-value problem. Analytical solutions of the problems are obtained for two models of an incompressible material: the neo-Hookean model and the Bartenev–Khazanovich model, and a model of a compressible semi-linear (harmonic) material. The dependence of the stress state as a whole on the adopted model of the material and the effect of the model of the material on the form of the stress singularity in the neighbourhood of a pole are investigated.