一种基于面-面局部搜索的接触算法

接触-碰撞算法是影响动态接触问题数值分析精度的重要因素,发展健壮、精确的局部搜索算法对提高数值模拟精度具有重要意义。为解决点-面接触搜索算法存在的盲区问题,提出了一种基于面-面的局部搜索算法,并发展了相应的接触力计算方法。新的接触算法以面心坐标与特征长度表征接触片,进行预搜索快速排除不会发生接触的潜在接触对;利用主从接触片的投影与侵入深度关系确定接触片间的接触状态;利用等参逆变换解析给出接触点,避免了方程组的迭代求解。典型算例与工程实例计算表明,本文算法消除了接触搜索的盲区,具有很好的健壮性与计算精度。     

一种基于面-面局部搜索的接触算法

接触-碰撞算法是影响动态接触问题数值分析精度的重要因素,发展健壮、精确的局部搜索算法对提高数值模拟精度具有重要意义。为解决点-面接触搜索算法存在的盲区问题,提出了一种基于面-面的局部搜索算法,并发展了相应的接触力计算方法。新的接触算法以面心坐标与特征长度表征接触片,进行预搜索快速排除不会发生接触的潜在接触对;利用主从接触片的投影与侵入深度关系确定接触片间的接触状态;利用等参逆变换解析给出接触点,避免了方程组的迭代求解。典型算例与工程实例计算表明,本文算法消除了接触搜索的盲区,具有很好的健壮性与计算精度。     

接触-碰撞算法研究进展

接触-碰撞广泛存在于实际工程问题中,是影响数值计算效率与计算精度的重要因素。本文针对变形体间接触-碰撞问题的显式有限元计算,介绍接触-碰撞算法近30年来取得的主要进展。首先,简要介绍接触-碰撞问题的界面离散模型;然后,从全局接触搜索、局部搜索、接触约束施加以及接触计算的并行化四方面详细阐述目前主要算法的基本思想与特点,并分析其优势与不足;最后,对接触-碰撞算法相关研究方向给出建议。     

一种基于莫顿码及镜像编码的平衡八叉树模型

在接触分析和动画模拟等网格规模庞大、需要实时更新的应用场景下,普遍采用莫顿码实现包围盒层次树结构的快速重构。但现有的层次树由于结构平衡性差,普遍存在搜索效率不稳定的问题,为此本文在莫顿码法的基础上提出了一种兼顾构建与搜索效率的平衡八叉树模型BOT树(Balanced Octree)。设计了镜像编码来保证树的上层节点均有8个分支,且同层树节点所含三角面数之差不超过1。实际算例表明,BOT树与现有模型OIOT树在CUDA并行框架下对比,构建加速比最高可达1.29×,且网格规模越大,BOT树构建效率的优势越明显。同时,与OIOT树相比BOT树的筛除率更高,在凸体接触和边缘接触算例中加速比分别达到1.13×和1.06×。     

接触-碰撞算法研究进展

接触-碰撞广泛存在于实际工程问题中,是影响数值计算效率与计算精度的重要因素。本文针对变形体间接触-碰撞问题的显式有限元计算,介绍接触-碰撞算法近30年来取得的主要进展。首先,简要介绍接触-碰撞问题的界面离散模型;然后,从全局接触搜索、局部搜索、接触约束施加以及接触计算的并行化四方面详细阐述目前主要算法的基本思想与特点,并分析其优势与不足;最后,对接触-碰撞算法相关研究方向给出建议。     

基于异步爬猴群算法的传感器优化布置方法研究

针对猴群算法中的重要步骤"爬过程"搜索盲目、效率较低的问题,提出了一种用于传感器优化布置的异步爬猴群算法。采用双重编码的方式,克服了原猴群算法只能解决连续变量优化问题的缺陷;利用猴群在搜索过程中的全局最优解和个体历史最优解的信息改进了爬过程的搜索模式,同时将异步变化学习因子引入到搜索模式中,通过调整猴子自身经验和社会群体经验在爬过程中所起的作用,来保持全局搜索和局部搜索的平衡,大幅提高了算法的搜索效率。文末以广州新电视塔为例,进行了参数敏感性分析以及传感器优化布置方案的选择。结果表明,异步爬猴群算法能较好的解决传感器优化布置问题,搜索效率较原猴群算法有了较大的提高。     

基于球形颗粒几何排列的离散元试样高效生成方法

在球体离散元数值模拟中,颗粒的初始排列状态是影响计算效率和计算结果的重要环节。本文采用前进面几何构造算法,提出了一种基于网格搜索的球形颗粒随机排列高效算法。通过求解空间三边方程,满足了粒径设置的任意大小的颗粒依次置入前进面的外侧,并与构成前进面的三个颗粒相互接触。为获得高体积分数的颗粒簇,该算法允许颗粒改变其粒径大小。采用颗粒网格化方法可以简化前进面的搜索,并由此提高排列效率。通过计算平均配位数、体积分数和二阶结构张量的特征值,对不同粒径比下得到的立方体试样进行了分析,得到试样配位数及体积分数均随着粒径比的增大而增大,且得到的试样为各向同性。此外,空间网格的大小和初始颗粒的生成点对随机排列的效率均会产生显著的影响。最后,对非规则铁路道砟进行了精细构造及压碎模拟,发现DEM模拟得到的应力-应变曲线与试验结果基本吻合,验证了该算法得到的颗粒试样在模拟道砟裂纹起裂、扩展等过程的有效性。     

基于免疫猴群算法的传感器优化布置方法研究

将生物界中的免疫机制引入到猴群算法中,提出了一种用于传感器优化布置的免疫猴群算法。采用双重编码的方式,克服了原猴群算法只能解决连续变量优化问题的缺陷;采用混沌搜索的方式初始化猴群位置,以保证猴子能够均匀分布,提高了算法的全局搜索能力;通过在爬过程中引入深度爬的方式,增强了算法的局部搜索能力;在爬过程结束后加入基于浓度选择的机制对猴群进行初次选择,并对位置最优的猴子进行免疫克隆操作,以此保证猴群的多样性;在望过程结束后加入基于适应度的二次选择,并对位置较差的猴子进行免疫疫苗注射,以此提高算法的收敛能力。文末以大连世贸大厦为例,进行了参数敏感性分析以及传感器优化布置方案的选择,结果表明,免疫猴群算法的搜索效率较原猴群算法有了大幅提高,能较好地解决传感器优化布置问题。     

引入退火机制的智能单粒子算法在复杂边坡最危险滑动面搜索中的应用

复杂边坡的安全系数可能存在多个局部极小值点,如何确定边坡的最小安全系数是复杂边坡稳定性分析中的一个关键问题。本文结合简化Bishop法,采用一种新的启发式全局优化算法——智能单粒子算法(ISPO)来搜索复杂边坡的最危险滑动面。为帮助该算法快速跳出局部极值点,本文将模拟退火(SA)机制引入到智能单粒子算法中,结合了两种算法各自的优点,提出了引入退火机制的智能单粒子算法SA-ISPO。将本文提出的SA-ISPO算法用于搜索两个复杂边坡的最危险滑动面,并与其它方法相比较,验证了SA-ISPO算法的优越性,该算法搜索效率高,计算结果不受搜索范围的影响,是一种较好的全局优化算法。     

基于协同爬猴群算法的传感器优化布置方法研究

基于协同进化的思想,提出了一种用于传感器优化布置的协同爬猴群算法。采用双重编码的方式,克服了原猴群算法只能解决连续变量优化问题的缺陷。在爬过程中引入采用猴群的整体行为来影响猴子搜索方向的聚群行为,以及利用全局最优猴子的位置来影响猴子搜索方向的追尾行为,通过对两种行为进行合理选择,有效提高了爬过程的搜索效率与速度。最后以大连国贸大厦为例,进行了参数敏感性分析以及传感器优化布置方案的选择,结果表明协同爬猴群算法的搜索效率较原猴群算法有大幅提高,能较好地解决传感器优化布置问题。     

A contact searching algorithm for contact-impact problems

A new contact searching algorithm for contact-impact systems is proposed in this paper. In terms of the cell structure and the linked-list, this algorithm solves the problem of sorting and searching contacts in three dimensions by transforming it to a retrieving process from two one-dimensional arrays, and binary searching is no longer required. Using this algorithm, the cost of contact searching is reduced to the order ofO(N) instead ofO(Nlog₂ N) for traditional ones, whereN is the node number in the system. Moreover, this algorithm can handle contact systems with arbitrary mesh layouts. Due to the simplicity of this algorithm it can be easily implemented in a dynamic explicit finite element program. Our numerical experimental result shows that this algorithm is reliable and efficient for contact searching of three dimensional systems. The project supported by the National Natural Science Foundation of China (59875045), and the State Key Laboratory of Automobile Safety and Energy Saving (K9705)     

Numerical design of multimodal axisymmetric hypersonic nozzles for wind tunnels

A method for design of hypersonic nozzles for wind tunnels is developed and implemented on the basis of solving direct problems with various models of the medium and numerical methods of integration of gas-flow equations. Multimodal nozzles for operation in Mach number ranges M _out =8–14 and M _out =14–20 satisfying specified requirements are designed.     

Large-scale computational fluid dynamics by the finite element method

Solution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier-Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods. For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector-parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector-parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP-8 and 9.2 Gflops on the NEC on SX3. For iterative methods, two approaches are developed. First, conjugate-gradient-like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side-by-side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence.     

The role of instrument compliance in normal force measurements of polymer melts

Schweizer et al. [J Rheol 48(6):1345–1363, 2004] showed nonlinear step shear rate data for a polystyrene melt (M _w=200 kg/mol, M _w/M _n=1.06, T=175°C). For different rheometers, cone angles, and sample sizes, the delayed normal force rise observed therein relative to a compliance-free reference N ₁ (from a thermodynamically consistent reptation model) is shown to depend on rheometer compliance characterized by the instrument stiffness K _A. K _A can be obtained from mapping N ₁ on the measured N _1,meas. or directly from mechanical contact measurement with a mismatch of 20–30%. The ranking of the stiffnesses found is K _A(RMS 800)>K _A(MCR 300)>K _A(ARES LR2). Once K _A is known, N _1,meas.-data can be corrected by solving the ill-posed Volterra equation involved in it. The correction shown for experiments with the 0.15-rad cone angle gives very good results. The characteristic decay time of the normal force after cessation of flow scales linearly with the axial response time t _a calculated from K _A, cone angle, and sample radius. The torque decay time is practically independent of t _a.Extended Version of a paper presented at the 2nd Annual European Rheology Conference in Grenoble, France, April 21–25, 2005.     

Peristaltic flow of a nanofluid in a non-uniform tube

The present analysis discusses the peristaltic flow of a nanofluid in a diverging tube. This is the first article on the peristaltic flow in nanofluids. The governing equations for nanofluid are modelled in cylindrical coordinates system. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Temperature and nanoparticle equations are coupled so Homotopy perturbation method is used to calculate the solutions of temperature and nanoparticle equations, while exact solutions have been calculated for velocity profile and pressure gradient. The solution depends on Brownian motion number N _b , thermophoresis number N _t , local temperature Grashof number B _r and local nanoparticle Grashof number G _r . The effects of various emerging parameters are investigated for five different peristaltic waves. It is observed that the pressure rise decreases with the increase in thermophoresis number N _t . Increase in the Brownian motion parameter N _b and the thermophoresis parameter N _t temperature profile increases. Streamlines have been plotted at the end of the article.     

The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field

The stability against small disturbances of the pressure-driven plane laminar motion of an electrically conducting fluid under a transverse magnetic field is investigated. Assuming that the outer regions adjacent to the fluid layer are electrically non-conducting and not ferromagnetic, the appropriate boundary conditions on the magnetic field perturbations are presented. The Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Reynolds number R_c, the critical wave number α_c, and the critical wave speed c_c are obtained for wide ranges of the magnetic Prandtl number P_m and the Hartmann number M. It is found that except for the case when P_m is sufficiently small, the magnetic field has both stabilizing and destabilizing effects on the fluid flow, and that for a fixed value of M the fluid flow becomes more unstable as P_m increases.     

Experimental study of the shock–bubble interaction with reshock

The interaction of a planar shock wave with a spherical density inhomogeneity is studied experimentally under reshock conditions. Reshock occurs when the incident shock wave, which has already accelerated the spherical bubble, reflects off the tube end wall and reaccelerates the inhomogeneity for a second time. These experiments are performed at the Wisconsin Shock Tube Laboratory, in a 9m-long vertical shock tube with a large square cross section (25.4×25.4 cm²). The bubble is prepared on a pneumatically retracted injector and released into a state of free fall. Planar diagnostic methods are used to study the bubble morphology after reshock. Data are presented for experiments involving two Atwood numbers (A = 0.17 and 0.68) and three Mach numbers (1.35 < M < 2.33). For the low Atwood number case, a secondary vortex ring appears immediately after reshock which is not observed for the larger Atwood number. The post-reshock vortex velocity is shown to be proportional to the incident Mach number, M, the initial Atwood number, A, and the incident shock wave speed, W _i.     

Finite element analysis of mode III steady crack growth in anisotropic hardening materials

In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk _ss/k_c varies appreciably with the anisotropic hardening parameterM and the hardening exponentN.     

Modelling of pressure–strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.