无网格法中SPH方法和有限元方法的对比分析

无网格法是近期发展起来的一种数值计算方法,根据形函数构造可分为多种样式.在此主要介绍了较常用的一种方法:光滑粒子法(SPH)并对这种方法的原理和计算过程与有限元方法进行对比.从而阐述SPH方法的特点,后边又用这两种方法对一个简单例子进行求解.     

光滑粒子流体动力学方法研究

光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)方法在模拟大变形问题时具有明显的优势,但是由于粒子的不连续性,致使其计算精度较低.文中对光滑粒子流体动力学方法中函数及其一阶导数的核估计进行详细研究.讨论传统的SPH方法和改进的CSPH (corrective smoothed particle hydrodynamics)方法的离散思想,在Taylor展开的基础上引入修正的MSPH(modified smoothed particle hydrodynamics)方法,并推导一维和二维情况下函数的核估计和函数的一阶导数核估计的离散形式.最后通过数值算例,对三种不同的SPH方法的计算精度进行详细比较,结果表明,CSPH和MSPH方法可以极大提高边界粒子的计算精度,在二维情况下,MSPH方法的计算精度要优于CSPH方法.     

基于SPH法的土壤切削刀具三维数值模拟及优化

为优化刀具结构,减小土壤切削的功耗,采用大型动力学软件LS—DYNA中的光滑粒子流体动力学（SPH）求解器,结合MAT147材料模型就松土刀具对土壤的切割过程进行了三维动态仿真。建立了反旋凿切的数值模拟模型;并结合正交试验法对松土铲耕作条件进行了仿真。仿真结果表明：利用SPH方法对土壤材料进行大应变、高应变率的变形计算是有效的;定性地得到了耕宽与耕深的关系,且结合相关理论将可以更全面合理地对松土铲刀具结构进行优化。     

SODF-SPH方法及其在热传导问题中的应用

在光滑粒子流体动力学(SPH)原理的基础上,通过泰勒级数展开提出了计算函数二阶偏导数的SODF-SPH方法。选用相等的粒子间距和相同的光滑长度对一维热传导问题进行了计算和模拟,与传统SPH方法进行了对比分析,结果表明新方法的精度高、收敛速度快且稳定性好;对二维和三维各种热传导问题进行了计算和模拟,与解析解进行了对比,结果表明新方法得到的计算结果与解析解吻合良好。新方法的计算过程能避免计算核函数导数,致使对核函数的要求降低,可选用更多的核函数且计算量较小,可在工程和数值计算中广泛应用。     

一对啮合齿轮模型离散成SPH粒子方法研究

利用连续体离散成均匀分布SPH粒子的思路,以渐开线直齿轮为例,通过其各部分曲线进行研究,确定齿轮齿根过渡曲线以及其他部分的参数方程,提出了三维齿轮和一对啮合齿轮模型离散成SPH粒子的方法和算法,编程实现了正确啮合一对齿轮模型离散成SPH粒子的SPH前处理程序。通过用SPH方法对齿轮传动中冲击、接触等问题进行计算和模拟,提供了一种较好的前处理平台。     

基于光滑粒子流体动力学的紫铜切屑形态研究

FEM存在网格变形和重构等诸多问题，难以解决切削过程中刀具前端材料出现的极端塑性变形以及高应变率问题。而无网格光滑粒子流体动力学方法能够解决FEM中由于网格变形所引起的畸变问题，从而模拟出各种材料的任意变形。目前针对SPH方法的切削仿真研究主要集中于工艺参数、材料本构等外部参数的敏感性分析，而对于SPH公式的选择、粒子密度等内部参数的敏感性分析较少。为此，本文通过使用Ls-Dyna仿真软件构建了基于SPH的紫铜正交切削仿真模型，并搭建了正交切削实验平台。针对显著影响紫铜切屑形态及计算精度的内部参数进行了研究，并与切削实验的切屑形态及切削力进行对比，结合仿真计算时间成本，最终确定粒子密度为216000pcs/mm³的重整化SPH更适合紫铜切削仿真实验研究。     

损伤零件冲击破坏的数值模拟

简要介绍了光滑粒子动力学方法的基本思想和基本方程，利用该方法编制程序对损伤零件的冲击破坏问题进行了数值模拟，并给出了用这种方法模拟三维冲击破坏的一个算例，对有关问题进行了讨论。     

陶瓷CBN砂轮地貌建模与磨削仿真

针对砂轮表面上磨粒形状的不规则性、尺寸的不确定性以及分布的随机性特点,采用随机空间平面切分实体的方法生成了具有实际磨粒几何特征的不规则多面体磨粒;提出了虚拟格子法,实现了磨粒空间位置的随机分布,构建了陶瓷CBN砂轮地貌仿真模型;采用有限元法和光滑粒子流体动力学法的耦合方法进行了砂轮地貌模型磨削仿真,通过切削层SPH粒子的运动情况,分析了磨粒的切削机理及工件表面的创成机理。     

风沙流结构的SPH模拟研究

风沙流结构是研究风沙流运动的重要内容,沙粒的起跳速度的分布对其有重要影响.这里使用光滑粒子流体动力学方法(Smooth Particle Hydrodynamics,简称SPH方法),建立了气体和沙粒的受力模型、沙粒之间的碰撞模型以及两相之间的耦合机制,分别模拟了两种粒径的沙粒在单一粒径沙粒条件下,在分布均匀的沙床面上...     

基于SPH法的CBN磨粒切削过程数值模拟

采用光滑粒子流体动力学法进行CBN磨粒切削过程仿真。该方法解决了网格法模拟材料分离时的网格束缚问题。通过切削过程中磨粒与工件材料的应力场变化以及离散SPH粒子的运动情况,分析了CBN磨粒的磨损机理以及工件材料的切削变形机理。研究结果表明:磨粒的顶部与挤压面棱边接触应力集中,易发生磨耗与微破碎磨损;工件材料受磨粒的推挤发生弹塑性变形而沿磨粒的侧向及前方隆起,并于磨粒的前方挤出而形成切屑。
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SPH method applied to high speed cutting modelling

The purpose of this study is to introduce a new approach of high speed cutting numerical modelling. A Lagrangian smoothed particle hydrodynamics (SPH)-based model is carried out using the Ls-Dyna software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control permits a “natural” workpiece/chip separation. The developed approach is compared to machining dedicated code results and experimental data. The SPH cutting model has proved is ability to account for continuous to shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Thus, comparable results to machining dedicated codes are obtained without introducing any adjusting numerical parameters (friction coefficient, fracture control parameter).     

基于SPH算法的驾驶室底部结构对爆炸冲击波响应数值仿真

针对地雷等简易爆炸装置在车辆驾驶室底部非接触爆炸问题,引入无网格光滑粒子流体动力学(Smoothed particle hydrodynamics,SPH)算法模拟爆炸冲击波作用下车辆底部结构的响应。以四边约束靶板为研究对象,分析靶板在爆炸冲击下的能量、应力变化和破坏形态,通过与传统的任意拉格朗日欧拉(Arbitrary Lagrangian-Eulerian,ALE)固流耦合分析法和经验公式计算结果对比,验证SPH算法应用于处理此类问题的可行性;利用SPH算法对爆炸冲击波作用下驾驶室底部结构进行数值仿真,分析车辆底部的油箱、电瓶支架、驾驶室地板、车架等关键结构的冲击响应,并与试验做出对比验证。仿真结果表明,基于SPH算法的爆炸仿真分析具有精度较高、建模简单、耗费计算资源少等优势,能够应用于爆炸冲击波作用下驾驶室底部板壳结构的响应研究,并为驾驶室底部结构抗爆炸设计提供参考。     

SPH方法在冲击破坏中的爆炸现象分析

由于SPH方法已被广泛应用到工程模拟的各个方面,虽然已有很大成功,但是还有很多的方面不成熟,其中之一就是爆炸现象,笔者对这种现象产生的原因进行了分析。     

不可压流体自由表面流动的SPH数值模拟

根据SPH方法的原理提出了一套模拟流体自由表面流动的方法,场变量及其导数通过核函数插值求取,不需进行差分,也不需要网格,时间积分采用分数步长法,避免了不可压条件带来的压力计算不稳定问题。对流项通过粒子的运动求解,完全消除了数值扩散和自由表面模糊问题。可以模拟飞溅、融合等复杂自由表面现象,并对水坝坍塌这一典型自由表面流动问题进行了模拟,模拟结果与试验吻合良好。     

SPH modeling of chip formation in cutting unidirectional fiber-reinforced composite

The machining of composites is of great interest in manufacturing today. To that end, it is necessary to calculate the cutting forces required and to predict the surface quality obtained. In the present work, the cutting zone of a unidirectional fiber-reinforced composite is simulated by the SPH method. The calculation results—specifically, the equivalent stress and the strain distribution—are compared with results obtained previously by the finite-element method and also with experimental data. The good agreement with experimental data indicates that the SPH method may expediently be used in simulating the cutting of composites.     

Analysis of Hagen-Poiseuille flow using SPH

This paper shows how to formulate the transient analysis of 2-dimensional Hagen-Poiseuille flow using smoothed particle hydrodynamics (SPH). Treatments of viscosity, particle approximation and boundary conditions are explained. Numerical tests are calculated to examine effects caused by the number of particles, the number of particles per smoothing length, artificial viscosity and time increments for 2-dimensional Hagen-Poiseuille flow. Artificial viscosity for reducing the numerical instability directly affects the velocity of the flow, though effects of the other parameters do not produce as much effect as artificial viscosity. Numerical solutions using SPH show close agreement with the exact ones for the model flow, but SPH parameter must be chosen carefully. Numerical solutions indicate that SPH is also an effective method for the analysis of 2-dimensional Hagen-Poiseuille flow.     

Incompressible SPH modeling and analysis of non-Newtonian power-law fluids,mixing in a microchannel with an oscillating stirrer

In the present study, a robust Incompressible smoothed particle hydrodynamics (ISPH) method, based on an advanced Smoothed particle hydrodynamics (SPH) discretization, is introduced to study the effects of the non-Newtonian power-law index and stirrer frequency on fluid mixing in an active micromixer that uses an oscillating stir-bar. Two Reynolds numbers (20 and 72) are considered, and more than 70 SPH simulations are carried out, in order to investigate the effects of the power-law index and stirrer frequency on fluid mixing. The results show that this active micromixer is more efficient at the lower power-law indices.     

Numerical simulations of impact flows with incompressible smoothed particle hydrodynamics

A 2D incompressible smoothed particle hydrodynamics (SPH) method is implemented to simulate the impact flows associated with complex free surface. In the incompressible SPH framework, pressure Poisson equation (PPE) based on the projection method is solved using a semi-implicit scheme to evaluate the correct pressure distribution. In this procedure, the PPE comprises the divergence-free velocity condition and density-invariance condition with a relaxation parameter. To test the accuracy and efficiency of the proposed incompressible SPH method, it was applied to several sample problems with largely distorted free surface, including 2D dam-break over horizontal and inclined planes with different inclination angles, as well as the water entry of a circular cylinder into a tank. We mainly focused on the time history of impact pressure on various positions of the solid boundary and temporal evolution of free surface profiles. The results showed reasonably good agreement with experimental data. However, further improvement is needed for extremely high impact flow.