元胞单元法

介绍一种力学计算方法--元胞单元法它将结构的整体求解变成局域分析,通过力的局域间的不平衡传递达到最终的整体平衡它对计算机容量要求低,在大规模计算方面具有良好的前景同时,由于借用了元胞自动机的思想,可形成一种高度并行的算法,适用于未来并行机的要求,是一种有发展潜力的数值方法,可望在大型结构和纳米力学的大规模摸拟方面得到应用文中介绍了元胞单元法的基本原理,将其用于平面问题分析,进行了数值试验,给出了计算步骤和结果,并对其优点和存在的问题进行了讨论.     

金属局部腐蚀的三维元胞自动机模型

针对环境作用下金属表面容易形成坑蚀而致使结构性能退化这一问题. 采用元胞自动机方法,建立描述腐蚀环境中金属表面坑蚀形成及演化的三维模型,对不同腐蚀溶液浓度和温度条件下结构表面蚀坑随时间的变化过程进行了模拟,为定量评估服役环境中结构的剩余强度及寿命提供可能.     

模拟Lotka-Volterra系统的元胞自动机

本文给出了用于模拟了Lotka-Volterra系统的元胞自动机．通过构造概率型元胞自动机，给出了Lotka-Volterra系统基元反应动力学方程．然后，通过系综平均，我们得到该元胞自动机具有Lotka-Vblterra系统的动力学行为．数值模拟再现了经典结果。     

大型边界元方程组的并行直接分块求解算法

针对大型边界元方程组和网络微机机群环境提出了一种并行直接分块求解算法，算法基于分块高斯-若当消去法的原理，采用内外存交互技术，并行分块消去方法，节点超行的卷帘存储方案和并行环状循环逐次修正策略，增大了解题规模，提高了计算速度。算例计算结果表明该算法具有较高的并行加速比和并行效率，适用于大型问题的边界元法求解。     

用移动元胞自动机法模拟杆式穿甲弹长细比对侵彻过程的影响

用移动元胞自动机法(movablecellularautomata,MCA)计算了质量和速度相同、长细比不同的杆 式穿甲弹对侵彻过程影响的实例,计算结果与实验符合。移动元胞自动机法能较好模拟爆炸和高速穿甲侵彻 中材料瞬间的变形﹑破碎和飞散过程。     

基于元胞自动机模型的C型交织区交通流特性

根据C型双侧交织区的车辆换道特征建立相应的换道规则,采用多车道元胞自动机模型研究交织区系统的交通流特性. 通过数值模拟得到了不同交织区长度下的相图,表明当主路和匝道交通流均为自由流时,交织区长度对系统影响不大,但当主路或匝道拥挤时,交织区长度的增加可以明显改善入口匝道的交通流状况. 进一步讨论了主路畅通而交织流量较大情形下主路上的车辆密度、速度和换道频率分布,发现换道集中在合流区和分流区附近,并造成相应路段上的局部拥堵.      

基于元胞自动机的变厚度薄壁梁侧向耐撞性优化设计方法

薄壁结构是汽车等运载工具的重要防护装置,除了其轴向防撞能力外,侧向耐撞性能分析与提升方式也非常重要。研究基于薄壁结构厚度合理分布的侧向耐撞性能提升方式和建立基于元胞自动机的变厚度薄壁梁侧向耐撞性优化方法。以汽车B柱受力环境和性能要求为设计需求,首先利用所建立的方法给出了连续变厚度的薄壁梁厚度分布设计,其性能较常规的等厚度薄壁梁最大侵入位移大幅下降(下降82%),验证了变厚度设计的有效性;然后,考虑单向变厚度便于柔性轧制工艺制成TRB,给出了轴向连续变厚度薄壁梁的厚度分布设计,该设计较等厚度梁最大侵入位移下降73%;与连续变厚度梁相比,在侵入位移降低量略小的情况下,实现了可制造性。设计实例表明本文提出的连续变厚度设计能够有效提高侧向耐撞性能,所建立的方法能够获得合理的厚度分布设计,是有效的耐撞性优化设计方法。     

无单元Galerkin法和边界元耦合法

无网格方法与有限元法或边界元法耦合是无网格方法处理边界条件的方法之一,在无网格方法中研究无网格方法与有限元法或边界元法耦合的研究显得非常重要.本文在无单元Galerkin法和边界元法的基础上,基于无单元Galerkin法子域和边界元法子域的界面上位移连续和面力平衡条件,提出了一种新的无单元Galerkin法和边界元法的直接耦合方法,对弹性力学问题详细推导了在整个求解域上的耦合公式.与以往的耦合法相比,这种方法简单直观,不需要增加新的耦合区域,也不需要建立新的逼近函数来保证界面位移的连续性.算例结果表明,该方法具有较好的计算精度.     

Wilson单元与广义杂交元等价性

本文用广义杂交法推出了Wilson单元及其修正模型,证明了Wilson不协调元与广义杂交元的等价性。     

三维自然单元法插值形函数的导数计算

根据Voronoi胞的几何性质,获得了积分点的二阶Voronoi胞顶点的表达式,并对各邻近结点相关的顶点进行排序以使其生成的二阶Voronoi胞切割面为凸多边形,从而获得各切割凸多边形面域的面积表达式;最后,基于复合函数链式求导法则,获得了三维自然单元法non-Sibson插值形函数导数的显式格式。相比Lasserre算法,该方法具有直观、便于编程且计算量小的特点。悬臂梁的算例结果进一步说明了该方法的可靠性,证实了文献[2,7,8]关于自然单元法具有比有限元中常应变单元更高的精度,理论上和双线性单元的精度同阶的结论。     

并行有限元网格生成方法及其应用

大型工程数值仿真中,在前处理阶段需要生成千万甚至亿量级的网格,传统的串行网格生成方法由于内存和时间的限制,难以处理如此规模的网格。针对此问题,本文提出了一种大规模网格并行生成方法。首先基于推进波前法对几何模型进行初始体网格划分,接着利用图论理论进行区域分解,并通过表面单元恢复保持其几何精度,然后通过分裂法进行网格的并行生成。将所述方法应用到实际大型工程数值仿真前处理阶段,结果表明所述方法可以获得较好的并行效率,同时所产生的网格质量可以满足后续计算需要。     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

Parallel finite element computation of unsteady incompressible flows

A parallel semi-explicit iterative finite element computational procedure for modelling unsteady incompressible fluid flows is presented. During the procedure, element flux vectors are calculated in parallel and then assembled into global flux vectors. Equilibrium iterations which introduce some ‘local implicitness’ are performed at each time step. The number of equilibrium iterations is governed by an implicitness parameter. The present technique retains the advantages of purely explicit schemes, namely (i) the parallel speed-up is equal to the number of parallel processors if the small communication overhead associated with purely explicit schemes is ignored and (ii) the computation time as well as the core memory required is linearly proportional to the number of elements. The incompressibility condition is imposed by using the artificial compressibility technique. A pressure-averaging technique which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady problems are solved to demonstrate the accuracy of the procedure. In all calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is sufficient to stabilize the convective term with no need for additional upwind-type dissipation. © 1998 John Wiley & Sons, Ltd.     

Parallel computing of discrete element method on multi-core processors

This paper describes parallel simulation techniques for the discrete element method (DEM) on multi-core processors. Recently, multi-core CPU and GPU processors have attracted much attention in accelerating computer simulations in various fields. We propose a new algorithm for multi-thread parallel computation of DEM, which makes effective use of the available memory and accelerates the computation. This study shows that memory usage is drastically reduced by using this algorithm. To show the practical use of DEM in industry, a large-scale powder system is simulated with a complicated drive unit. We compared the performance of the simulation between the latest GPU and CPU processors with optimized programs for each processor. The results show that the difference in performance is not substantial when using either GPUs or CPUs with a multi-thread parallel algorithm. In addition, DEM algorithm is shown to have high scalability in a multi-thread parallel computation on a CPU.     

An iterative parallel algorithm of finite element method

In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.     

板壳畸变单元的无网格和有限元自动耦合方法

板壳大变形时单元的严重畸变会使计算精度降低。无网格局部Petrov-Galerkin法是一种真正的无网格方法,能够消除网格畸变,但比有限元法计算效率低。根据板壳网格畸变的局部性特点,利用过渡单元法,基于板壳网格质量,建立了板壳的网格严重畸变区域由有限元分析切换为无网格分析的自动耦合算法,实现了有限元法和无网格局部彼得罗夫．迦辽金法的耦合。应用实例表明：通过自适应耦合,既能发挥有限元法计算效率高的特点,又能发挥无网格法适合大变形分析、没有网格畸变造成计算困难的特点。     

PARALLEL ANALYSIS OF COMBINED FINITE／DISCRETE ELEMENT SYSTEMS ON PC CLUSTER

A computational strategy is presented for the nonlinear dynamic analysis of largescale combined finite/discrete element systems on a PC cluster. In this strategy, a dual-level domain decomposition scheme is adopted to implement the dynamic domain decomposition. The domain decomposition approach perfectly matches the requirement of reducing the memory size per processor of the calculation. To treat the contact between boundary elements in neighbouring subdomains, the elements in a subdomain are classified into internal, nterfacial and external elements. In this way, all the contact detect algorithms developed for a sequential computation could be adopted directly in the parallel computation. Numerical examples show that this implementation is suitable for simulating large-scale problems. Two typical numerical examples are given to demonstrate the parallel efficiency and scalability on a PC cluster. The project supported by the National Natural Science Foundation of China (10372114) and the Engineering and Physical Sciences Research Council (EPSRC) of UK (GR/R21219)     

基于区域分解的并行有限元程序及其在水下爆炸中的应用

基于MPI标准定义的消息传递接口实现了显式动力学有限元程序的并行计算.通过基于Hilbert空间填充曲线的区域分解算法,实现各区域的独立运算和区域之间共享数据的相互通信.利用程序对水下爆炸自由场中的冲击波传播规律进行了数值模拟,并通过对不同进程数下的并行加速比进行测试,验证了程序的并行效率.     

面向对象的无单元法

介绍了一种用C 进行的面向对象无单元方法程序设计;定义了一些关键的类并将有些类设计成类等级,从而建立了包含权函数、基函数和形函数在内的面向对象无单元法程序类库,在此过程中考虑了无单元法与有限元法的某些联系,保留并重用了面向对象有限元法程序中的一些类。本文提供了一种无单元法大型分析软件开发新途径。