Discrete element simulation of dynamic behaviour of partially saturated sand

The discrete element method (DEM) together with the finite element method (FEM) in LS-DYNA was employed to investigate the dynamic behaviour of sand under impact loading. In this approach, the partially saturated sand was modelled in DEM with capillary forces being taken into account through an implicit capillary contact model, while other solids were simulated using FEM. A slump test was first performed with dry sand to calibrate the contact parameters in DEM. Low velocity impact tests were then conducted to investigate the effect of water saturation on the shape and height of sand piles after impact, and to validate the simulations. It was found in the experiments that an increasing water saturation (in the range between 10 and 30 %) affected the height of sand pile for a given drop height due to an increasing cohesion between particles. The simulations captured the experimental ejecta patterns and sand pile height. Finally, a low confinement split Hopkinson pressure bar test from earlier literature was modelled; the DEM–FEM simulations could reproduce the trends of experimentally observed stress–strain curves of partially saturated sand under high strain rate loading, indicating that it was feasible to model dynamic behaviour of dry and wet sand with low saturation (<20 %) in LS-DYNA; however, a number of questions remain open about the effect of grain shape, grain crushing and viscosity.     

基于GPU并行的锥体导管架平台结构冰激振动DEM-FEM耦合分析

该文为分析海冰与锥体海洋平台的相互作用,采用离散元（DEM）-有限元（FEM）耦合方法建立冰激海洋平台结构的耦合模型。通过具有粘结-破碎性能的球体离散单元对海冰的漂移及破碎现象进行计算,海洋平台锥体部分采用平板型壳单元构造,其整体构架及锥体内部的加劲肋采用梁单元构造,即建立壳单元与梁单元组合的锥体海洋平台有限元模型。为提高DEM-FEM耦合算法的计算规模和效率,发展了离散单元与平板型壳单元接触算法及GPU并行环境下参数传递算法。基于此耦合模型分别讨论了平台结构的冰载荷、冰激振动以及锥体应力分布,并与相关实测数据进行对比,为寒区锥体海洋平台的结构设计提供有益的参考。     

Identification of Constitutive Material Model Parameters for High-Strain Rate Metal Cutting Conditions Using Evolutionary Computational Algorithms

Advances in plasticity-based analytical modeling and finite element methods (FEM) based numerical modeling of metal cutting have resulted in capabilities of predicting the physical phenomena in metal cutting such as forces, temperatures, and stresses generated. However, accuracy and reliability of these predictions rely on a work material constitutive model describing the flow stress, at which work material starts to plastically deform. This paper presents a methodology to determine deformation behavior of work materials in high-strain rate metal cutting conditions and utilizes evolutionary computational methods in identifying constitutive model parameters. The Johnson-Cook (JC) constitutive model and cooperative particle swarm optimization (CPSO) method are combined to investigate the effects of high-strain rate dependency, thermal softening and strain rate-temperature coupling on the material flow stress. The methodology is applied in predicting JC constitutive model parameters, and the results are compared with the other solutions. Evolutionary computational algorithms have outperformed the classical data fitting solutions. This methodology can also be extended to other constitutive material models.     

基于DEM-FDM耦合的普通铁路碎石道床-土质基床界面接触应力分析

引入离散元法（DEM）-有限差分法（FDM）耦合算法对普通铁路碎石道床-土质基床的界面应力进行分析。首先,基于激光扫描以及室内三轴试验,实现碎石道砟颗粒二维精细化离散元建模,并通过设置界面单元进行道砟与土两类不同介质层间速度与力的相互传递,实现离散元法与有限差分法耦合,建立了轨枕-碎石道床-连续土体耦合模型,并通过现场实测结果验证模型的合理性。在此基础上,计算列车通过时耦合模型中基床动应力分布特征,讨论轨枕-道床接触状态对其影响,并将计算结果与轨枕-道床-基床的整体有限元模型的计算结果进行对比。结果表明,轨枕-道床未完全密贴接触状态下,道床中力链呈离散型传递,反之,道床中力链呈向下扩散发展;两种接触状态下,基床表面应力分布差别显著,但是应力峰值接近。耦合模型得到的基床表面应力峰值显著高于有限元模型的计算结果;耦合模型中因道砟散体特性引起的基床表面局部应力集中,在路基中的影响深度约为道砟最大粒径（63 mm）的8倍,即近似基床表层深度。     

A strategy to determine DEM parameters for spherical and non-spherical particles

In Discrete element method (DEM) simulations the choice of appropriate contact parameters is significant to obtain reasonable results. Particularly, for the determination of DEM parameters for non-spherical particles a general straightforward procedure is not available. Therefore, in a first step of the investigation here, methods to obtain the friction and restitution coefficients experimentally for single particles [Polyoxymethylene (POM) spheres and quartz gravel] will be introduced. In the following, these predetermined DEM coefficients are used as initial values for the adjustment of bulk simulations to respective experiments. In the DEM simulations, the quartz gravel particles are represented by non-spherical particles approximated by clustered spheres. The best fit approximation of the non-spherical particles is performed automatically by a genetic algorithm. In order to optimize the sliding and rolling friction coefficients for DEM simulations, the static and dynamic angle of repose are determined from granular piles obtained by slump tests and rotating drum experiments, respectively. Additionally, a vibrating plate is used to obtain the dynamic bed height which is mainly influenced by the coefficient of restitution. The adjustment of the results of the bulk simulations to the experiments is conducted automatically by an optimization tool based on a genetic algorithm. The obtained contact parameters are later used to perform batch-screening DEM simulations and lead to accurate results. This underlines the applicability of the in parts automated strategy to obtain DEM parameters for particulate processes like screening.     

Numerical and experimental studies of the base pressures beneath stockpiles

Stockpiles are common for storage of bulk solids in many industrial sectors. One interesting phenomenon is that there is a significant dip of the base pressure beneath the apex of the pile which may have significant implications in the design of stockpile facilities and related support structures. This paper presents a numerical and experimental study of this phenomenon. Experiments have been conducted to measure the base pressure distribution under a stockpile formed with iron ore pellets and significant central stress minimum was revealed. Continuum analysis using the finite element method (FEM) was conducted to simulate the stress distribution in the test pile. It showed the critical importance of progressive pile development and nonlinear constitutive models. To investigate the underlying mechanisms further, simulations using the discrete element method (DEM) were conducted, which related well to the FEM predictions and revealed key aspects of the inter-particle force patterns. Both the FEM and DEM predictions show a dip in the base pressure distribution which is in agreement with test results, and reveal new key features of the mechanics of such piles.     

冲击环境下PBGA焊点动态特性分析

根据焊点成形理论和影响焊点可靠性因素对PCB和PBGA256组件进行有限元建模，并以此为基础对其进行模态分析及瞬态冲击动态响应分析，得出了最大应力应变在PGBA256上分布曲线；并根据实际情况简化得出焊点局部模型应变分布，从而找出焊点最易断裂失效的区域。最后，通过激光测振系统测得的实验模态和计算结果比较，表明所建立的有限元模型，可作为以后进行焊点疲劳寿命估计和焊点形态优化的基础。     

基于模态参数及BAS-PSO优化算法的软基水闸有限元模型参数修正方法

正确合理的有限元模型对于软基水闸结构健康监测及性能评估至关重要,但水闸有限元模型参数的不确定性使得建立的水闸有限元模型难以准确地反映水闸结构真实的动力学特性,该文结合模态参数和基于天牛须搜索算法的粒子群(BAS-PSO)优化算法,提出了一种软基水闸有限元模型参数修正方法。选择对水闸模态参数影响较大的弹性模量和密度作为待修正参数,建立反映软基水闸待修正参数和模态参数之间非线性关系的基于遗传算法的支持向量回归(GA-SVR)代理模型;提出基于GA-SVR代理模型计算模态参数与水闸振动模态参数之间相对偏差最小的目标函数,构建软基水闸有限元模型参数修正的最优化数学模型;提出一种BAS-PSO优化算法来求解最优化数学模型,克服了局部最优和收敛速度慢的问题。通过软基水闸物理模型实例表明,修正的有限元模型计算的模态参数与水闸识别模态参数在数值上比较吻合,该文方法合理可靠且具有良好的可行性,可为软基水闸有限元模型参数修正提供一条新思路。     

Identification of Parameters in 2D-FEM of Valve Piping System within NPP Utilizing Seismic Response

Nuclear power plants (NPP) contain plenty of valve piping systems (VPS’s) which are categorized into high anti-seismic grades. Tasks such as seismic qualification, health monitoring and damage diagnosis of VPS’s in its design and operation processes all depend on finite element method. However, in engineering practice, there is always deviations between the theoretical and the measured responses due to the inaccurate value of the structural parameters in the model. The structure parameters identification of VPS within NPP is still an unexplored domain to a large extent. In this paper, the initial 2Dfinite element model (FEM) for VPS with a DN80 gate valve was updated by utilizing seismic response. The objective function used in the model updating procedure is the vibration control equation error of the VPS. The experimental results show that the updated 2D-FEM can accurately predict the original dynamic characteristic of the VPS. It was also found the Rayleigh damping coefficients corresponding to the VPS vary slightly with the change in seismic excitation amplitude. The research displayed the complete procedure of updating the complex structured initial FEM by utilizing seismic response, and the results show that the parameters can be accurately identified even if the seismic response used for updating merely contained the fundamental frequency information of the structure.     

风、列车作用下斜拉桥索-梁相关振动对拉索疲劳可靠性的影响

以实际大跨度斜拉桥为研究对象,研究了随机风、列车作用下发生的索-梁相关振动对拉索疲劳可靠性的影响。使用编制的动力有限元计算程序,建立了大跨度铁路斜拉桥全桥3维精细有限元模型,计算了斜拉桥全桥在风、列车动力作用下的振动响应,分析了全桥索-梁相关振动的特性。建立了列车交通荷载概率模型,根据桥位处风速统计数据资料建立了桥梁的风荷载概率模型,对拉索的应力谱进行了计算。依据损伤理论,使用Monte-Carlo方法开展了拉索在风、列车动力作用下的疲劳可靠度分析。研究结果表明:在斜拉桥日常运营状态中,风、列车作用下索-梁相关振动不会导致拉索共振,索-梁相关振动是拉索疲劳可靠性下降的主要原因;对于拉索在长期动力荷载下的疲劳失效概率,风场作用占比很小,列车作用占比较大;各个拉索的成桥状态索力影响了列车作用下的拉索应力幅,进一步影响了斜拉桥在长期动力作用下拉索的疲劳可靠性。     

Optimization of a pipe end upsetting process

A method is proposed for the optimization, by finite element analysis, of design variables of sheet metal forming processes. The method is useful when the non-controllable process parameters (e.g. the coefficient of friction or the material properties) can be modelled as random variables, introducing a degree of uncertainty into any process solution. The method is suited for problems with large FEM computational times and small process window. The problem is formulated as the minimization of a cost function, subject to a reliability constraint. The cost function is indirectly optimized through a “metamodel”, built by “Kriging” interpolation. The reliability, i.e. the failure probability, is assessed by a binary logistic regression analysis of the simulation results. The method is applied to the u-channel forming and springback problem presented in Numisheet 1993, modified by handling the blankholder force as a time-dependent variable.     

A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending

A stochastic finite element method (SFEM) is developed for accurate structural reliability analysis. Using the second-order three-moment reliability analytical model, this method takes into account such random factors as load, material parameters and especially geometry randomness. The calculation of the bending fatigue strength reliability of a cantilever beam is carried out as a numerical example to verify the present method. Monte-Carlo FEM and SFEM based on the first-order second-moment model are used in the example to compare with the proposed method. By incorporating the fatigue theory of gears, the present method is then used to analyze the bending fatigue strength reliability of a spur gear. The effects of random variables' coefficient of variation and skewness and the gear's correction factor (not random variable) on the gear's reliability are also investigated.     

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading‐history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large‐scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross‐scale understanding of granular media. The developed framework is first benchmarked by a simulation of single‐element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non‐coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.     

基于模型修正的空间变异边坡可靠度分析方法

空间变异边坡可靠度计算需要进行多次重复性边坡稳定性分析,常用的边坡稳定性分析极限平衡方法（LEM）计算效率较高而有限元方法（FEM）可捕捉真实的边坡失效机制,边坡可靠度评价中如能充分利用这两者的优势将具有重要的工程价值。该文在发展考虑参数空间变异性边坡可靠度分析的一阶可靠度方法（FORM）基础上,提出基于模型修正的空间变异边坡可靠度分析方法,引入一修正系数将基于LEM的简化极限状态面逐渐修正为基于FEM的准确极限状态面,最后基于修正系数和LEM安全系数计算公式采用线抽样法计算边坡失效概率。通过一个考虑参数空间变异性的摩擦/粘性土坡算例验证提出方法的有效性,并探讨土体参数空间变异性和黏聚力与内摩擦角之间互相关性对边坡可靠度的影响。结果表明:提出方法的边坡可靠度计算精度与基于FEM子集模拟方法一致,但是计算效率远远大于后者,尤其对于低概率水平边坡可靠度问题,从而为解决考虑土体参数空间变异性的低概率水平边坡可靠度问题提供一条新的途径。     

基于响应面法的摊铺机压实系统参数优化

摘要：对摊铺机样机的试验研究发现沿熨平板长度方向振幅差值较大。为了改善熨平板振幅的不均匀性,将熨平板作为柔性体,建立了摊铺机压实系统的刚柔混合动力学模型;选取振捣梁质量以及振动器偏心轴的质量和偏心距的乘积为设计变量,以熨平板上节点振幅差为优化目标,通过基于正交设计的响应面方法,借助数值分析,建立优化变量和优化目标间的函数关系,采用遗传算法进行优化。优化后熨平板上节点振幅差减少了83%,各节点振幅均匀性大大改善。     

三维实体结构NURBS等几何分析

等几何分析是近年来在有限元法基础上发展起来的一种新的数值方法,它消除了有限元的几何误差,具有高阶连续性。该文研究了三维结构等几何分析中NURBS几何体的表示方式及载荷、约束的施加方法,分别从计算精度和仿真效率两个方面对比了等几何分析的计算结果与有限元法一阶单元和二阶单元的计算结果,展示了等几何分析相对于标准有限元法的优势,并以厚壁圆筒模型算例验证了等几何分析的实用性。将NURBS单元应用于几何形状精度要求高的齿轮和变截面圆筒,数值结果表明三维NURBS等几何分析方法在复杂三维结构的仿真计算中具有较好的灵活性和适用性,可得到连续的应力场,有望在工程中得到广泛应用。     

Discrete Element Method for the thermal field: Proof of concept and determination of the material parameters

The physical behaviour of materials and complicated components is nowadays numerically predicted by using the Finite Element Method (FEM). Another method, older than the finite element idea, is the Discrete Element Method (DEM), with which it is possible to make continuum-based calculations not only in the mechanical field but also in the thermal field, as will be shown in this paper.One major drawback of the FEM is that continuum-based methods are unable to include the stochastically distributed microscopic effects in the macroscopically oriented calculations. The Discrete Element Method is one method with which these effects can be considered.For making realistic fracture and life time predictions for components at high temperatures, it is important to adapt the DEM for the thermal field. This paper describes the mathematical proof of the 2D Discrete Element Method (or Lattice Model) for the thermal field. It will specifically be shown that the heat flux inside the framework can be transferred to the heat conduction equation. Furthermore, some examples demonstrate how the heat flux can be calculated with this method and how the corresponding material parameters are found and implemented. Also, as will be shown in this paper, anisotropic or orthotropic heat flux effects can be integrated in the DEM model.     

弹性DEM方法在杆系结构中的应用研究

基于颗粒离散元方法（DEM）,结合杆系结构的特点,提出了一种适于杆系结构问题分析的DEM模型。对颗粒元相应的质量和转动惯量计算公式进行了修正;通过能量等效原理推导了杆系DEM模型分析时弹簧接触刚度系数表达式;将瑞利阻尼引入到DEM方法之中,给出了阻尼常数计算公式并用算例进行了验证。将该方法应用于杆系结构弹性分析,包括静动力与几何非线性大变形问题的空间框架结构和网壳结构等多个算例,计算结果与有限元方法结果吻合良好。DEM方法的特点是将动力分析和几何非线性分析自动包含在运动方程的计算之中,不用组集刚度矩阵,无需迭代求解。杆系DEM模型非常适宜处理杆系结构大变形及动力非线性问题,尤其是在结构进入强非线性之后的模拟分析。     

基于响应面法的结构动力学模型修正

为了获得精确的结构动力学模型,提出了响应面和优化相结合的方法。利用参数化模型和优化拉丁方试验设计获取样本点构造多项式响应面模型,最小二乘法确定多项式系数并检验响应面的拟合精度。用响应面计算结果与实验结果的误差构造目标函数,自适应模拟退火算法来优化修正响应面参数,将修正后的参数值带入有限元模型得到修正模型。以欧洲航空科技组织的基准模型GARTEUR飞机模型为算例,对比修正前后模态频率,结果表明修正后的模型在测试频段和预测频段具有良好的复现和预测能力,进而验证了基于响应面法与优化方法相结合的结构动力学有限元模型修正的有效性。     

岸桥起重机随机风振疲劳可靠性分析

基于时域方法研究岸桥起重机的风振疲劳可靠性问题。采用谐波叠加法给出了符合Davenport风速谱的多维脉动风速时间历程,基于Bernoulli方程得到相应的风压时间历程,并将相应的风压荷载作用于有限元模型,采用雨流计数法处理结构关键点的应力响应。基于疲劳失效的Basquin方程、Miner线性累积损伤准则和Goodman平均应力修正方程导出疲劳累积损伤的概率模型。考虑平均风速的概率分布,提出了基于概率累积损伤机制的风振疲劳可靠度和可靠性寿命计算方法,为岸桥起重机的风振疲劳可靠性分析作了一些有益的探索和研究。