混凝土细观力学分析程序中的快速算法与并行算法设计

针对一套混凝土细观力学分析程序,在分析其计算方法与计算效率的不足之后,提出了采用稀疏矩阵与稀疏向量技术来高效实现有限元刚度矩阵装配过程的算法,并采用双门槛不完全Cholesky分解预条件技术与CG法相结合来高效地求解稀疏线性方程组。之后,从整体上提出了一个将有限单元分布与未知量分布有机结合的并行算法设计方案,并分别针对刚度矩阵装配、双门槛不完全Cholesky分解、稀疏矩阵与稠密向量相乘、稀疏向量相加等核心算法,进行了相应的并行算法设计。最后,在由每节点2 CPU的8个Intel Xeon节点采用千兆以太网连成的机群上,针对两个混凝土数值试样进行了数值实验,第一个试样含44117个网格点与53200个有限单元,第二个试样含71013个网格点与78800个有限单元;对第一个试样,原串行程序进行全程567次加载计算需要984.83小时约41天,采用文中串行算法后,模拟时间减少到22531秒约6.26小时,采用并行算法在16个CPU上的模拟时间进一步降为3860秒约1.07小时。对第二个试样,原串行程序进行全程94次加载计算需要467.19小时约19.5天,采用文中串行算法后,模拟时间减少到11453秒约3.18小时,采用并行算法在16个CPU上的模拟时间进一步降为1704秒约28.4分钟。串行算法的改进与并行算法的设计大大缩短了计算时间,对加快混凝土力学性能的分析研究具有重要意义。     

Algorithms for controlling fatigue tests of airplanes

The efficiency of algorithms for automatic control of forces prescribed in the test program is analyzed by an example of a large-aspect-ratio wing considered as a beam loaded by aerodynamic and inertial forces.     

Comparison of different implementation algorithms for HiSS constitutive models in fem

Relative accuracy, stability and efficiency of four popular algorithms to implement elasto-plastic constitutive models in non-linear finite element procedures have been compared. Elastic Predictor–Plastic Corrector (EP–PC) method, Plastic Predictor–Plastic Corrector (PP–PC) method, Implicit Integration (Implicit) method and Modified Euler (ME) method wereused to implement Hierarchical Single Surface (HiSS) δ₀1 model into the general purpose finite element program ABAQUS. First, these algorithms were used outside the finite element program to simulate various triaxial stress paths. After that, they were used in ABAQUS to simulate two strip footings: (a) displacement controlled rigid footing and (b) load controlled flexible footing. The effect of the sub-strain increment size on the accuracy, stability and efficiency of each algorithm during these simulations have been compared. Implicit Method and ME performed well for some problems but performed poorly on others. EP–PC and PP–PC methods performed equally well for all the problems. This also showed the importance of testing algorithms under various stress paths and boundary value problems to assess their relative performance.     

Segregated finite element algorithms for the numerical solution of large-scale incompressible flow problems

This paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large-scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non-symmetric advection–diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.     

On the Numerical Integration of the Rolling Ball Equations Using Geometrically Exact Algorithms

ABSTRACT

In this paper, new types of numerical integration algorithms developed by the authors are described. The main aim of the algorithms is to numerically integrate differential equations that evolve on geometric objects, such as the rotation group and Euclidean group. The algorithms provide iterates that lie on the prescribed geometric object, either exactly or to some prescribed accuracy, independent of the order of the algorithm. In this sense the algorithms can be called geometrically exact integration algorithms. The paper also describes the application of these new algorithms to the nonholonomic dynamic equations that describe a ball rolling on a flat table, using the kinematic evolution in the Euclidean group.     

An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.     

非陀螺找北系统的计算机仿真研究

阐述了对设计的一种非陀螺找北系统进行计算机仿真的原理、方法。提出了降低系统噪 声影响、提高估计精度的多位置采样和多周期平均算法，并通过仿真对其算法原理进行了验 证。仿真程序采用多线程技术，实现了实时测量，缩短了系统反应时间。     

无网格局部Petrov-Galerkin方法的并行计算研究

研究了无网格局部Petrov-Galerkin方法MLPG(Meshless Local Petrov-Galerkin Method)的并行算法与并行实现过程。将MLPG方法推广到弹性动力学问题,研究了MLPG方法中节点搜索、积分点搜索、数值积分及方程组求解等过程的并行算法,并给出了MLPG方法并行计算的具体实现过程。两个数值算例验证了MLPG并行算法的有效性;计算结果表明,MLPG方法的并行计算具有很好的并行性能和可扩展性。     

基于节点的局部网格生成算法

讨论了基于节点的有限元方法的网格生成算法及其产生的不一致性问题,提出了基于D e launay三角剖分的唯一性来克服网格不一致性现象的思想,并建议使用局部区域分割方法合理地确定探索圆半径,使中心节点的探索圆包含它的所有卫星点,进而确保算法无不一致性。理论分析和算例表明了该方法的可靠性及有效性。     

A General Methodology for Full-Field Plastic Strain Measurements Using X-ray Absorption Tomography and Internal Markers

Probing the strain locally and throughout the bulk of various materials has long been of interest in Materials Science. This article presents a general methodology for assessing the plastic strain in terms of the displacement gradient tensor throughout the bulk of opaque samples. The method relies on a homogenous distribution of marker particles throughout the bulk of a sample, markers which are detected through the application of synchrotron X-ray tomography. Making use of the morphology of individual markers, motion of individual markers is tracked during deformation allowing the local displacement field to be determined throughout the bulk. The local displacement gradient tensor is derived from the displacement field. Spatial resolution is directly related to marker particle density in the sample, here 30 μm. The accuracy of the displacement gradient tensor calculation is dependent on the accuracy with which each marker position is determined and is shown to be in the range from 0.005 to 0.012. The software implementation of the procedures and algorithms presented in this work has been collected to form the “3Dstrain” program package which is intended to be free for use by the scientific community. It is available at under GNU General Public License.     

On the extraction of stress-intensity factors from near-tip photoelastic data

Existing algorithms and a new algorithm called ‘quadratic’, for extracting stress-intensity factors (SIF) from frozen-stress photoelastic data are evaluated for application to near-tip data in three-dimensional problems. It is shown that for this class of problems, modifications to some of the existing algorithms may be necessary, in some cases, in order to ensure reliable SIF values. But that for all the algorithms, the two-parameter form of the governing equations of linear-elastic fracture mechanics (LEFM) is sufficient for use with near-tip data, even for complex three-dimensional geometries. Paper was presented at the 1983 SEM Spring Conference on Experimental Mechanics held in Cleveland, OH on May 15–20.     

Variational base and solution strategies for non-linear force-based beam finite elements

This paper presents the variational bases for the non-linear force-based beam elements. The element state determination of these elements is obtained exactly from a two-field functional with independent stress and strain fields. The variational base of the non-linear force-based beam elements implemented in a general purpose displacement-based finite element program requires the inclusion of independent displacement field in the formulation. For this purpose, a three-field functional is considered with independent displacement, stress, and strain fields. Various local and global solution strategies come out from the mixed formulation of the beam element, and these are shown to yield the algorithms presented for non-linear force formulation beam elements in literature; thus removing any doubts on their variational bases. The presented numerical examples demonstrate the accuracy and robustness of the solution algorithms adapted for mixed formulation elements over popularly used displacement-based beam finite elements even for large structural systems.     

Methods of analytical mechanics in the constrained adaptive identification problems

The application of analytical mechanics methods to the problem of adaptive identification is discussed. The estimated constant parameters satisfy nonlinear equations considered as parametric constraints. Some modifications of identification algorithms are proposed to satisfy such constraints.     

Unwedge(2.35)程序在分析块体稳定性中的应用

Unwedge (2 .35 )程序在原Ver.1.0的基础上做了改动 ,程序的功能增强。根据作者使用该程序的经验 ,结合工程实践介绍了Unwedge (2 .35 )程序的基本原理方法、及该版本的缺陷。     

MAS 5．0结构分析和优化设计系统

ＭＡＳ是一个兼有结构分析、优化设计和图形处理的现代有限元程序系统，适用于多部门进行工程项目和产品的现代设计．本文简要介绍ＭＡＳ５．０新版软件的组成和功能，系统特点及应用情况．     

Simulation of free and forced convection incompressible flows using an adaptive parallel/vector finite element procedure

The numerical simulation of complex flows demands efficient algorithms and fast computer platforms. The use of adaptive techniques permits adjusting the discretisation according to the analysis requirements, but creates variable computational loads that are difficult to manage in a parallel/vector program. This paper describes the approach adopted to implement an adaptive finite element incompressible Navier–Stokes solver on the Cray J90 machine. Performance measurements for the simulation of free and forced convection incompressible flows indicate that the techniques employed result in a fast parallel/vector code. Copyright © 1999 John Wiley & Sons, Ltd.     

基于MEMS技术的微型惯性导航系统的发展现状

根据美国 DARPA(the Defense Advanced Research Projects Agency)资助项目的概况,介绍了微电子机械系统(MEMS)惯性传感器领域的新进展,对 DARPA 的特别项目 MEMS-INS(Inertial Navigation System)的进展状况进行了说明。详细描述了惯性技术、导航技术领域内前沿研究机构研究 MEMS INS 的路线,总结了微型导航技术系统算法的研究现状。最后,对 MEMSINS 的发展进行展望,指出 MEMS INS 的发展方向。过去的发展趋势表明:微型惯性技术将向芯片级的超小型 MEMS IMU(Inertial Measurement Unit)和 MEMS INS 以及组合导航的发展方向。     

对动力修正方法SDM3.0的探讨与改进

本文运用理论分析、实验与计算的结果对引进的美国SMS公司的结构动力修正软件SDM3.0作了比较详细的探讨,指出了SDM3.0的优点、局限性与使用范围.提出了改进这一软件的方法,研制了相应的软件.结果表明:改进后的方法及相应的软件是有效和成功的.     

Exploring alternative approaches to computational fluid dynamics

This paper discusses advances in two areas which may have the potential to impact future simulation capabilities through advanced algorithms. This includes spectral multigrid (MG) solvers for high-order accurate spatial discretizations and efficient MG solvers for kinetic-based schemes. Preliminiary evidence is given illustrating the promise of these approaches for application to engineering simulations.