Calculation of Drag Force on an Object Settling in Gas-Solid Fluidized Beds

Gas-solid fluidized beds can be used for dry beneficiation of minerals. Estimation of the drag force on separated materials is important for the design and operation of separators. Previous research was based on the empirical correlation or on the hypothesis that fluidized beds behave as a Newtonian fluid. However, much experimental evidence showed that the hypothesis of Newtonian fluid was suspect. The drag forces on spheres passing through fluidized beds were calculated using the Bingham fluid model. The plastic viscosity and yield stress of a fluidized bed can be obtained by measurement of the terminal settling velocity of spheres. The relationship between drag coefficient (C D ), sphere size (d o ), settling velocity (u t ), bed bulk density ( 𝜌 b ), plastic viscosity (), and yield stress ( 0 ) is expressed as C D = 24/ Re m (1 + 0.15 Re 0.687 m ), Re m = d o u t 𝜌 b /( + 0 d o /3 u t The calculated results agree well with the experimental data.     

FE Analysis of Contractant Shear Zones in Loose Granular Materials

The paper focuses on the formation of contractant shear zones in initially loose cohesionless granular materials subject usually to continuous densification. For a simulation of the mechanical behaviour of a granular material during monotonous deformation paths, a micro-polar hypoplastic constitutive model was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The FE investigations of shear localization were carried out with initially very loose quartz sand during four different rate boundary value problems: shearing of an infinite layer between two very rough walls, plane strain compression under constant lateral pressure, biaxial compression with rigid and deformable boundaries and passive earth pressure on a horizontally translating retaining wall. The calculations were carried out with a simple random distribution of the initial void ratio under conditions of large deformations and curvatures.     

Behaviour of granular bodies in induced shear zones

This paper deals with the behaviour of granular bodies in induced shear zones. Shearing of an infinite narrow layer of sand between two very rough boundaries under conditions of free dilatancy is numerically modelled with a finite element method and a hypoplastic constitutive relation within a polar (Cosserat) continuum. The relation can reproduce the essential features of granular bodies during shear localisation. The material constants are easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, mean grain diameter, layer height, pressure level and grain roughness on the thickness of induced shear zones. In addition, the effect of dilatancy constraint on shear localisation is investigated. The results are also compared to solutions within a non-polar continuum. The FE-calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in shear zones and their thickness is mainly affected by the initial void ratio, the mean grain diameter and the layer height. Received: 16 November 1999     

FE Stress Analysis of Thick Composite Laminates with a Hole in Bending

In this work, the stress analysis of isotropic and ortotropic laminae both with a hole and without a hole and laminated both with a hole and without a hole composite plates have been examined using the finite element method. In order to solve the problem, a computer program has been written by using characteristics of eight-node isoparametric plane element. The calculations have been tested on various composite and steel materials by this program. The results have been shown in diagrams and tables and compared with literature. It was observed that the stress distributions in the plate with a hole was totally different from the plate without a hole. The analyses have showed that, the elastic stresses have been gradually reduced as moving from the first layer to the second.     

大尺寸KDP晶体生长开裂的尺度效应分析

在人工生长大尺寸KDP(磷酸二氢钾,KH2PO4)晶体过程中晶体会发生开裂现象,尤其是晶体生长到400mm左右时晶帽下端容易出现裂纹.为了研究KDP晶体的生长过程中的开裂机制,采用有限元方法模拟该晶体的生长过程,重点分析了晶体在不同生长尺寸的应力场分布规律,结果表明生长过程中晶体内部应力分布存在明显的尺度效应.当KDP晶体生长达到400mm时,晶帽下部受力逐渐由受压状态转变为受拉状态,根据KDP晶体材料抗拉不抗压的性质,此时开裂的机率增大.这一发现为下一步深入研究晶体生长开裂的损伤力学机制和寻找KDP晶体生长中的防裂措施奠定了基础.     

FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.     

一类桥式直接耦合柔性机构的刚度与应力分析

分析了一类桥式直接耦合柔性机构的精确的刚度和应力模型.分别采用伪刚体模型和卡氏第二定理推导了该柔性机构理论刚度模型,利用两个理论模型与有限元模型的结果进行对比,并采用正交实验法全面分析了柔性铰链的寄生刚度和旋转刚度的精度对其刚度性能的影响.研究结果表明：该柔性机构的寄生刚度影响较小,误差贡献率小于3%;旋转刚度的精度影响较大,通过选择精确的旋转刚度公式可以得到精确的理论刚度模型,同有限元结果相比其误差在t/r〈0.65范围内小于8%;与设计实验及其对应的有限元结果的误差分别为4%和3.96%,验证了刚度模型的正确性.基于刚度模型推导了该柔性机构的应力模型,运用正交实验法与有限元结果进行对比,误差小于4%,验证了应力模型的正确性.     

An Edge-Based Smoothed Discrete Shear Gap Method Using the C0-Type Higher-Order Shear Deformation Theory for Analysis of Laminated Composite Plates

The edge-based smoothing discrete shear gap method (ES-DSG3) using three-node triangular elements is combined with a C⁰-type higher-order shear deformation theory (HSDT) to give a new linear triangular plate element for static, free vibration, and buckling analyses of laminated composite plates. In the ES-DSG3, only the linear approximation is necessary, and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are calculated relying on smoothing domains associated with the edges of the triangular elements through an edge-based strain smoothing technique. Using the C⁰-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. The numerical examples demonstrated that the ES-DSG3 show remarkably excellent performance compared to several other published elements in the literature.     

钢箱提篮拱桥整桥模态试验研究

随着大型柔性桥梁建设的迅速发展 ,其长期安全运行的健康监测的评估得到很大关注。通过试验模态分析对验证设计、建立结构的动力学模型以及桥梁安全运行状态的评估具有重要意义。拱桥桥面主梁与拱结构耦合振动 ,其模态试验比斜拉桥更加困难。本文通过我国首座建成的云南小湾钢箱提篮拱桥模态试验和竣工试验 ,提出了一种节省试验成本的基于环境激励下桥梁模态试验方法 ,取得了拱桥整体振动的较为正确的模态频率、阻尼及较理想振型 ,与有限元计算基本吻合。     

Analysis of nets with hexagonal mesh using triangular elements

The calculation of net shapes is achieved using the finite element method. A triangular element is developed for the modelling of the net. The main hypotheses are that the strain in each triangular element is constant, that the hexagonal meshes have three directions of twine, and that the twines are elastic. The forces due to the tension in twines are described and calculated by a direct method. The results of the model based on such triangular elements are provided. The comparison with a model where each twine is described as an elastic bar, is quite good. Copyright © 2003 John Wiley & Sons, Ltd.     

筒仓内散体静态屈服的研究

认为仓贮散体为服从Mohr—Coulomb屈服准则的理想弹塑性材料 ,散体与仓壁之间的摩擦属于Coulomb摩擦接触问题。就刚性筒仓讨论研究了静态时影响散体进入屈服状态的有关因素 ,提出了一种由散体临界内摩擦角来判断静态散体是否进入屈服状态的方法 ,并用有限元法做了数值模拟     

微细铣削加工过程中微毛刺形成机理的模拟与实验分析

研究了采用硬质合金微铣刀铣削加工硬铝合金微槽结构时微毛刺的形成机理．建立了三维微细铣削加工硬铝合金A12024-T6的有限元模型,利用该模型动态模拟微毛刺的形成过程．分析了不同进给量与切削刃钝圆半径比值下微毛刺的形成机理,动态模拟了微槽加工过程中切削参数及切削刃钝圆半径变化对微毛刺影响的变化规律．仿真结果表明,随着每齿进给量、背吃刀量及切削刃钝圆半径的增加,微毛刺的尺寸随之增大;切削刃钝圆半径与最大有效应力是影响微毛刺尺寸的主要因素．微细铣削加工过程中,毛刺顶端所受最大有效应变明显比常规铣削加工过程中的最大有效应变高,呈现出显著的尺寸效应．通过微细铣削加工微槽实验,获得了切削参数及切削刃钝圆半径变化对微毛刺形成的影响变化规律,验证了相应有限元模型的正确性．通过数值模拟与实验方法获得了切削刃钝圆半径与毛刺尺寸（毛刺高度和毛刺厚度）的关系曲线,实验与仿真结果最大误差不超过9．8％．进一步验证了所建立的三维有限元模型适于研究并预测毛刺形成机理及毛刺尺寸的变化规律．     

Conservation properties of a time FE method—part II: Time‐stepping schemes for non‐linear elastodynamics

In the present paper one‐step implicit integration algorithms for non‐linear elastodynamics are developed. The discretization process rests on Galerkin methods in space and time. In particular, the continuous Galerkin method applied to the Hamiltonian formulation of semidiscrete non‐linear elastodynamics lies at the heart of the time‐stepping schemes. Algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals. We newly introduce the ‘assumed strain method in time’ which enables the design of energy–momentum conserving schemes and which can be interpreted as temporal counterpart of the well‐established assumed strain method for finite elements in space. The numerical examples deal with quasi‐rigid motion as well as large‐strain motion. Copyright © 2001 John Wiley & Sons, Ltd.     

Behavior of Granular Material in Packed Bed Under Influence of Gas Injected Through a Nozzle

Cavity size hysteresis is an important phenomenon that affects the aerodynamics of any packed bed reactor significantly. Using the discrete element method approach, the mechanism of cavity size hysteresis in the presence of gas flow has been studied. The modeling results on cavity size have been compared with experiments and show a reasonable agreement. It is found that bed history, interparticle interaction forces, and gas drag all play an important role in the formation of cavities. The bed porosity in the decreasing gas velocity case was always found higher than the increasing gas velocity. The net gas drag at any location above the gas injection point in the bed decreases as the gas velocity is increased. It is also found that the change in interparticle interaction forces with gas flow rate is a major cause of the hysteresis phenomenon.     

Bounds for element size in a variable stiffness cohesive finite element model

The cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction–separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack‐tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi‐phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross‐triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al₂O₃ ceramic and in an Al₂O₃/TiB₂ ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour. Copyright © 2004 John Wiley & Sons, Ltd.     

折叠式托盘箱货架弯曲的有限元分析及试验验证

目的市场上的托盘箱普遍根据经验设计,其设计周期长,成本高。拟研究利用有限元模拟托盘箱性能的可行性。方法先利用三维软件Solidwokrs完成托盘箱的建模,再导入有限元分析软件Workbench模拟其货架弯曲性能,根据模拟结果修改模型,直至满足要求后进行打样制造,然后进行实际托盘箱样品的实验。结果托盘箱货架弯曲的实验结果和模拟结果总体上吻合度较高,托盘上5个试验位置挠度的相对误差随着载荷的增大而逐渐减小,并趋于稳定。结论使用有限元软件Workbench来进行托盘箱结构的设计和性能模拟分析是可行且有效的。     

一种可折叠环保型包装箱的结构设计与分析

目的为了降低物流成本,解决快递包装箱日益增长的需求量与社会资源浪费和物流成本增加的矛盾。方法采用国际标准化模数尺寸作为基础,使用模数分割法进行箱体尺寸设计,并通过统计电商物流包装箱尺寸分布情况初步确定设计尺寸。基于模块化设计和绿色设计,采用可降解材料聚丙烯设计一种可折叠环保型包装箱方案,不仅可以方便折叠与回收,同时通过模块化设置改变箱体尺寸,以满足不同规格商品的包装需求。采用第四强度理论和有限元分析的方法,进行力学分析验证其可靠性。结果箱体在长度方向可实现模块化长度调整,当箱体尺寸为260 mm×180 mm,高度为180 mm,壁厚为5 mm,圆角半径为5 mm时综合性能最优,货物在静止堆码和运输加减速的工况下,箱体最大应力均小于聚丙烯的压缩屈服强度,尺寸设计可靠。结论可折叠环保型快递包装箱具有较好的收纳性、可回收性、环保性、防潮性和灵活性,同时具有良好的力学性能,保证了使用的可靠性,有效地解决了快递包装箱不能循环利用、商品过度包装、安全性能及抗压性能较差等问题。     

Direct numerical simulation of saturated deformable porous media using parallel hybrid Lattice–Boltzmann and finite element method

Numerical techniques for modeling saturated deformable porous media have mainly been based on mixture theory or homogenization techniques. However, these techniques rely on phenomenological relationships for the constitutive equations along with assumptions of homogeneous and isotopic material properties to obtain closure. Direct numerical simulations of the multiphasic problem for flow in deformable porous media avoid such assumptions and thus can provide significantly accurate understanding of the physics involved. They serve as a tool to investigate the constitutive relationships in complex geometries. They also allow the validation of the existing mixture theory models and determine their limitations. In this work, a parallel hybrid method using Lattice Boltzmann Method (LBM) for fluid phase and Finite Element Method (FEM) for solid phase is used for direct numerical simulation of saturated deformable porous media. The method provides a number of unique features including scalability on distributed computing necessary for such a problem. The method has been validated for modeling fluid–structure interactions in complex geometries against a number of experimental and analytical solutions. Further some challenging problems has been chosen to show the capability of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

驾驶室内部噪声分析与阻尼降噪

基于有限元和边界元方法,运用ANSYS和SYSNOISE软件建立驾驶室声—固耦合有限元模型和声学边界元模型,计算在指定工况下壁板的振动和驾驶员右耳旁的声压级。在此基础上,进行面板声学贡献度分析,确定对驾驶员右耳声压贡献突出的壁板。通过采用沥青型阻尼材料对壁板进行减振降噪处理,有效地降低驾驶员右耳旁噪声。     

Size Sensitivity for the Reliability Index in Stochastic Finite Element Analysis of Damage

The direct differentiation method is applied to the estimation of statistical size effect behaviour in quasi-brittle solids. The scale factor is included in the finite element model and the autocorrelation function. Particular attention is paid to the proper differentiation of the Nataf transformation, which has been chosen to convert the basic random variables into a set of uncorrelated, standard normal variables. The predictive possibilities of the presented algorithm provide a valuable insight in the actual mechanisms responsible for failure. It can be evaluated to what extent the scale factor sensitivity of the failure probability is influenced by the phenomena related to the material disorder or the deterministic size effect.