A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

Parallelized Implementation of the Finite Particle Method for Explicit Dynamics in GPU

As a novel kind of particle method for explicit dynamics,the finite particle method(FPM)does not require the formation or solution of global matrices,and the evaluations of the element equivalent forces and particle displacements are decoupled in nature,thus making this method suitable for parallelization.The FPM also requires an acceleration strategy to overcome the heavy computational burden of its explicit framework for time-dependent dynamic analysis.To this end,a GPU-accelerated parallel strategy for the FPM is proposed in this paper.By taking advantage of the independence of each step of the FPM workflow,a generic parallelized computational framework for multiple types of analysis is established.Using the Compute Unified Device Architecture(CUDA),the GPU implementations of the main tasks of the FPM,such as evaluating and assembling the element equivalent forces and solving the kinematic equations for particles,are elaborated through careful thread management and memory optimization.Performance tests show that speedup ratios of 8,25 and 48 are achieved for beams,hexahedral solids and triangular shells,respectively.For examples consisting of explicit dynamic analyses of shells and solids,comparisons with Abaqus using 1 to 8 CPU cores validate the accuracy of the results and demonstrate a maximum speed improvement of a factor of 11.2.

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

Numerical Simulation of Bubble Formation at a Single Orifice in Gas-fluidized Beds with Smoothed Particle Hydrodynamics and Finite Volume Coupled Method

A coupled method describing gas–solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds.Solid particles are traced with smoothed particle hydrodynamics,whereas gas phase is discretized by finite volume method.Drag force,gas pressure gradient,and volume fraction are used to couple the two methods.The effect of injection velocities,particle sizes,and particle densities on bubble growth is analyzed using the coupled method.The simulation results,obtained for two-dimensional geometries,include the shape and diameter size of a bubble as a function of time;such results are compared with experimental data,previous numerical results,and other approximate model predictions reported in the literature.Moreover,the flow profiles of gas and particle phases and the temperature distribution by the heat transfer model around the forming bubble are also discussed.All results show that the coupled method efficiently describes of the bubble formation in fluidized beds.The proposed method is applicable for solving gas–solid two-phase flow in fluidization.

Modeling of contact surface morphology and dust particles by using finite element method

The effect of dust particles on electric contacts and a hazardous size range of hard dust particles using a rigid model were discussed before. As further research, elastic-plastic model of finite element analysis was established in this work, which is closer to real condition. In this work, the behavior of large size and small size particles, and the influence of particles hardness were investigated. The calculating result of small-size particles presents a general hazardous size coefficient for different contact surface morphology; for large-size particles, it presents a hazardous size coefficient for complicated composition of the dust. And the effect of the dust shape is also discussed.

Geotechnical particle finite element method for modeling of soilstructure interaction under large deformation conditions

The possibilities of the particle finite element method(PFEM)for modeling geotechnical problems are increasingly evident.PFEM is a numerical approach to solve large displacement and large strain continuum problems that are beyond the capabilities of classical finite element method(FEM).In PFEM,the computational domain is reconfigured for optimal solution by frequent remeshing and boundary updating.PFEM inherits many concepts,such as a Lagrangian description of continuum,from classic geomechanical FEM.This familiarity with more popular numerical methods facilitates learning and application.This work focuses on G-PFEM,a code specifically developed for the use of PFEM in geotechnical problems.The article has two purposes.The first is to give the reader an overview of the capabilities and main features of the current version of the G-PFEM and the second is to illustrate some of the newer developments of the code.G-PFEM can solve coupled hydro-mechanical static and dynamic problems involving the interaction of solid and/or deformable bodies.Realistic constitutive models for geomaterials are available,including features,such as structure and destructuration,which result in brittle response.The solutions are robust,solidly underpinned by numerical technology including mixedfield formulations,robust and mesh-independent integration of elastoplastic constitutive models and a rigorous and flexible treatment of contact interactions.The novel features presented in this work include the contact domain technique,a natural way to capture contact interactions and impose contact constraints between different continuum bodies,as well as a new simplified formulation for dynamic impact problems.The code performance is showcased by the simulation of several soil-structure interaction problems selected to highlight the novel code features:a rigid footing insertion in soft rock,pipeline insertion and subsequent lateral displacement on over-consolidated clay,screw-pile pull-out and the dynamic impact of a free-falling spherical penetrometer into clay.

A GPU-Based Parallel Algorithm for 2D Large Deformation Contact Problems Using the Finite Particle Method

Large deformation contact problems generally involve highly nonlinear behaviors,which are very time-consuming and may lead to convergence issues.The finite particle method(FPM)effectively separates pure deformation from total motion in large deformation problems.In addition,the decoupled procedures of the FPM make it suitable for parallel computing,which may provide an approach to solve time-consuming issues.In this study,a graphics processing unit(GPU)-based parallel algorithm is proposed for two-dimensional large deformation contact problems.The fundamentals of the FPM for planar solids are first briefly introduced,including the equations of motion of particles and the internal forces of quadrilateral elements.Subsequently,a linked-list data structure suitable for parallel processing is built,and parallel global and local search algorithms are presented for contact detection.The contact forces are then derived and directly exerted on particles.The proposed method is implemented with main solution procedures executed in parallel on a GPU.Two verification problems comprising large deformation frictional contacts are presented,and the accuracy of the proposed algorithm is validated.Furthermore,the algorithm’s performance is investigated via a large-scale contact problem,and the maximum speedups of total computational time and contact calculation reach 28.5 and 77.4,respectively,relative to commercial finite element software Abaqus/Explicit running on a single-core central processing unit(CPU).The contact calculation time percentage of the total calculation time is only 18%with the FPM,much smaller than that(50%)with Abaqus/Explicit,demonstrating the efficiency of the proposed method.

Form Finding and Collapse Analysis of Cable Nets Under Dynamic Loads Based on Finite Particle Method

This paper presents form finding and collapse analysis of cable net structure under strong wind using the finite particle method(FPM).As a kind of particle method,the theoretical fundamentals of the FPM are given.Methods to handle geometric and material nonlinearities of cable element are proposed.The fracture criterion and model for cable element are built to simulate the failure of cable nets.The form-finding and load analysis of two cable nets are then performed in order to initialize the successive of nonlinear analysis.The failure progress of cable nets under dynamic loads is simulated,and the dynamic responses of the typical fracture element are given in details.Analyses of the energy variations during the collapse process also show the failure mechanisms of cable nets,which is useful for the structure collapse resistance design.The numerical applications highlight the capability of the proposed procedure to solve complicate collapse problems with the FPM.

Numerical Investigation of Particle Rebound Characteristics with Finite Element Method

In this work, investigation of particle rebound characteristics due to impact with surface of a target material is presented. The rebound of a spherical particle after impact on a planar surface was analyzed in detail. Specifically, the coefficient of restitution of the particle under various impact conditions was investigated numerically. This study has been conducted by carrying out a series of FEM-based (finite element method) simulations using ANSYS Autodyn software. First, a summary about the state of the art and the theoretical models for the elastic collisions were reviewed. Afterwards, the impact of an aluminum oxide particle on an aluminum alloy target surface was modeled. Using the Autodyn tool, the results were compared and validated by the experimental results of Gorham and Kharaz [1]. Selection of an appropriate equation of state (EOS) and a strength model for each material had a strong effect on the results. For both materials, the Shock EOS was applied for the final simulations. As the strength model, the Johnson-Cook and the elastic model were used, respectively. The agreement of the obtained numerical results with the experimental data confirmed that the proposed model can precisely predict the real behavior of the particle after the impact, when the material models are properly chosen. Furthermore, the effects of impact velocity and impact angle on the rebound characteristics of the particle were analyzed in detail. It was found that the selection of the exact value of friction coefficient has a drastic effect on the prediction of restitution coefficient values, especially the tangential restitution coefficient.

Finite Difference Method of Modelling Groundwater Flow

In this study, finite difference method is used to solve the equations that govern groundwater flow to obtain flow rates, flow direction and hydraulic heads through an aquifer. The aim therefore is to discuss the principles of Finite Difference Method and its applications in groundwater modelling. To achieve this, a rectangular grid is overlain an aquifer in order to obtain an exact solution. Initial and boundary conditions are then determined. By discretizing the system into grids and cells that are small compared to the entire aquifer, exact solutions are obtained. A flow chart of the computational algorithm for particle tracking is also developed. Results show that under a steady-state flow with no recharge, pathlines coincide with streamlines. It is also found that the accuracy of the numerical solution by Finite Difference Method is largely dependent on initial particle distribution and number of particles assigned to a cell. It is therefore concluded that Finite Difference Method can be used to predict the future direction of flow and particle location within a simulation domain.

Improvement of the Viscous Penalty Method for Particle-Resolved Simulations

A numerical study of the parameters controlling the viscous penalty method is investigated to better set up Particle-Resolved Direct Numerical Simulations (PR-DNS) of particulate flows. Based on this analysis, improvements of the methods are proposed in order to reach an almost second order convergence in space. The viscous penalty method is validated in Stokes regime by simulating a uniform flow past a fixed isolated cylinder. Moreover, it is also utilized in moderate Reynolds number regime for a uniform flow past a square configuration of cylinder and compared in terms of friction factor to the well-known Ergun correlation.

基于非结构网格粒子输运的蒙特卡罗模拟计算研究

传统的构造实体几何的建模方式不能满足复杂几何输运、多物理耦合计算和大尺度核辐射效应模拟等问题,目前MCNP程序允许在非结构化的网格下跟踪粒子,它是作为一个网格空间嵌入在传统的构造实体几何之中,非结构网格几何采用有限元程序ABAQUS创建,使用MCNP的径迹长度估计器计算非结构网格单元内的输运结果,并在非结构网格上执行单元对单元的跟踪,结果可以输出到ABAQUS或者Paraview进行可视化和其他物理分析。本文分析了两种典型的基准实验:Ueki固定源和Godiva临界源问题,模拟结果表明,UM几何的运行时间和与CSG几何的计算偏差与输入网格单元的数量、单元的阶数成正比,同样阶数的四面体比六面体结果误差更小,本文的非结构网格计算结果与传统的构造实体几何结构结果具有很好的一致性。

一种适用宽速域冲击的明胶鸟弹数值建模方法

明胶鸟弹在不同撞击速度下表现出不同的响应特性。为解决传统明胶鸟弹本构表征方法在不同速度范围内不能通用的问题,开展了330 g明胶鸟弹以70~190 m/s速度、60°或90°入射刚性铝合金平板试验,记录了冲击力数据及撞击形貌。结果表明,随着撞击速度的提高,鸟弹碎裂得更充分,碎块体积减小。利用LS-DYNA建立了自适应FEM-SPH(finite element method-smoothed particle hydrodynamics)鸟体模型。依据试验结果反演得到一组鸟体本构参数:切线模量为1.33MPa,剪切模量为115.95MPa,Murnaghan状态方程参数γ为10.49,k_(0)为69.77 MPa,体积模量为246.4 MPa,失效塑性应变为1.15,初始屈服应力为0.21 MPa。仿真结果与试验结果具有很好的一致性,冲击力峰值的相对误差在2%以内,冲量的相对误差在10%以内。自适应FEM-SPH鸟体模型具有比SPH模型和拉格朗日模型更高的精度。由自适应模型得到的Hugoniot压强与理论结果具有相同的变化趋势,滞止压强与理论值较接近。

含大石块泥石流冲击作用下框架结构房屋动力响应研究

基于光滑粒子流体动力学-有限元法(smoothed particle hydrodynamics-finite element method,SPH-FEM)耦合的数值方法,分别从结构破坏形态、冲击力时程、关键点位移和速度、系统能量等方面,研究含大石块泥石流冲击作用下框架结构房屋的动力响应和破坏机理。计算结果表明:SPH-FEM耦合方法能够较好地模拟泥石流冲击爬高、绕流扩散、淤积稳定过程。考虑了三种泥石流强度等级,在低、中强度冲击情况下,框架房屋填充墙受到破坏,房屋结构整体保持稳定;在高强度冲击情况下,可以观察到框架房屋的逐步倒塌过程,框架柱损坏模式体现了剪切破坏或塑性铰链失效机制。对于房屋结构而言,泥石流的冲击破坏能力主要来自龙头的冲击力,龙身冲击力相对于龙头降幅约34.2%,大石块的集中作用是结构柱体局部破坏的主要原因。系统能量主要通过泥石流动能转化为结构内能(17.8%)和摩擦耗能(82.8%)。

基于PFEM法的黄土地基振杆密实过程大变形分析

采用粒子有限元方法(PFEM)及结构性土的本构模型,对振杆密实法加固砂质黄土地基的大变形过程进行了数值模拟研究,分析了振杆贯入过程中周围土体的位移场、应力场、速度场以及塑性体应变等分布规律,揭示了砂质黄土地基深层振动密实机理.结果表明:现场实测和数值模拟获得的地面垂直振动速度峰值变化趋势较为一致,验证了粒子有限元方法的可靠性;垂直激振的振杆能够同时引起土体垂直方向和水平方向上位移场、应力场和速度场的变化;在距振源水平距离5R(R为振杆半径)范围内,土颗粒以半梭形向外扩展并趋于密实,同时水平应力大幅增加并产生预压效果;以塑性体应变作为加固范围的评价标准,结果表明土体径向加固范围随振杆贯入深度增加而略有增大,最大径向加固范围约为3.2R,且振杆底端以下1R~2R范围亦有密实效果.

冷喷涂金属颗粒变形行为数值模拟研究进展

理解冷喷涂中的颗粒变形和沉积行为一直是科学工作的焦点。由于颗粒撞击基底后的瞬时变形行为难以通过实验观测,因此多数研究工作聚焦于数值模拟。总结了一些颗粒撞击基底的建模方法,在前人研究的基础上,针对每个模型的原理及优缺点,分析了每个方法的适用场景,给出了改善模型的方法。综述了颗粒特性、入射角度、气体预热温度等对颗粒变形行为的影响,其中粒径大小、颗粒形状等是影响颗粒变形行为的主导因素,因此重点探讨了颗粒特性的影响。颗粒的撞击变形是影响冷喷涂涂层残余应力分布的重要因素,对涂层残余应力的相关数值模拟研究进行了综述,分析了颗粒变形与颗粒残余应力的关系。最后就目前冷喷涂残余应力建模较单一的形势,探讨了如何建立一种新模型以分析涂层残余应力。

高超声速火箭橇凿削磨损机理分析

针对高超声速下火箭橇运行过程中凿削磨损产生的机理模糊不清问题,基于有限元-光滑粒子流体动力学法(FEM-SPH法),利用有限元软件ABAQUS构建了三维火箭橇靴-轨模型,FEM-SPH法是一种既能保证计算精度,又能克服网格畸变的新型模拟方法。在该模型中,滑靴和轨道所使用的材料分别为VascoMax 300钢、AISI 1080钢,并赋予各自材料属性,通过设定航向速度为2000 m/s,竖直速度为2.5 m/s以及温度为673 K,模拟了高超声速下靴-轨凿削磨损现象的演变过程。模拟结果表明:凿削磨损是在高温高应力作用下和靴-轨之间形成嵌入式结构后,经过持续地破坏滑靴底部所产生的,最终形成泪滴状蚀坑。进一步分析表明,竖直速度和温度的增加都会提高凿削发生的概率。在航向速度为2000 m/s、初始温度为673 K时,竖直速度超过1.50 m/s就会发生凿削现象;在航向速度为2000 m/s、竖直速度为2.5 m/s,温度超过293 K就会发生凿削现象。该研究成果不仅有助于高超声速下靴-轨凿削磨损的产生机理进一步完善,还为高超声速火箭橇试验的安全发射提供了新的理论支持。

水平振动式滚磨光整加工残余应力离散元有限元耦合仿真与实验研究

为探究水平振动式滚磨光整加工对零件表面残余应力的影响,提出一种适用于动态零件的离散元有限元(DEM-FEM)耦合仿真方法。分析了振动周期内颗粒运动状态以及颗粒间平均接触力的变化,构建了颗粒与零件间的随机接触模型,开展了不同振动参数下的残余应力仿真,并进行了实验验证。研究结果表明:随着振动强度的增大,容器内颗粒运动更加剧烈,颗粒与零件间有效法向接触力发生概率及均值增大,导致零件表面残余压应力呈增大趋势。残余应力仿真值与实验值对振动参数的响应趋势一致,误差在3.6%~11.3%之间。

基于PMADS与共轭优化法的单元上下料口布局与AGV配置联合优化

在具有有限能力物料储运系统的单元流水式车间中,针对单元上料与下料(P/D)口位置布局与物料搬运AGV数量配置的联合优化问题,建立了以最小化平均运输总成本和AGV配置成本为目标的单元P/D口布局与AGV配置联合优化模型。由于P/D口布局与AGV配置具有不同的优化特点,为了提高算法效率和结果的质量,提出一种嵌入共轭优化法和粒子群优化的网格自适应直接搜索算法(PMADS),在优化过程中分别对新解的P/D口布局及对应的AGV配置进行再优化。将所提算法与其他对比算法应用于某精密制造企业新工厂规划项目,结果显示PMADS算法在性能和求解质量上均优于其他算法,有效解决了单元流水式车间单元P/D口布局与AGV配置的联合优化问题。结果验证了所提算法在求解车间单元P/D口布局与AGV配置问题上的有效性、高效性及实用价值,所提共轭优化法加强了算法搜索的方向性,提高了算法效率和解的质量。