最优化算法的收敛准则

收敛准则是最优化算法的重要组成部分，其选择得好与坏将直接影响到算法的成功与否以及收敛得快与慢。现有常用的收敛准则基本上是建立在前后迭代点的逼近和它们相应函数值的逼近是否达到一定的精度要求以及迭代点处函数梯度是否接近于零的基础上的。它们各自有自己的适用范围。但它们的共同特点是对迭代终止点的性质不能做出判断。本文在总结和分析现有算法收敛准则的基础上，借助于正定矩阵、一维优化方法中对分法和黄金分割法，提出了新的算法收敛准则。算例结果表明，这些收敛准则是有效实用的。     

各向异性本构关系在板料成形数值模拟中的应用

对几种能表达面内各向异性的屈服准则Hill、Barlat-Lian、Barlat进行了比较。以弹性变形服从各向同性广义虎克定律的情况下，给出了基于张量算法推导的弹塑性本构关系的一般表达式，并由此导出了相应屈服准则的弹塑性本构关系的显式表达。借助ABAQUS软件本构模块用户子程序接口，分别实现了这些屈服准则在ABAQUS的嵌入。以模拟方形盒的拉延过程为例，分析了不同的屈服准则在板料成形过程数值模拟中的应用。模拟结果表明，基于弹塑性本构关系一般表达所列出的相应屈服准则的显式表达式是正确的；在采用壳元来模拟板料成形时，采用Barlat准则的模拟结果和采用Barlat-Lian准则的结果差别不大。     

采用二次等参体元时的接触判据

当二次等参体元用于分析接触问题时,接触面上节点集中接触力不同号给建立接触判据造成困难。本文建立了由节点集中接触力计算接触面上分布接触力节点值的方法,从而可顺利建立接触判据。此方法已成功应用于工程中的弹性固体接触问题分析,文末给出了一个计算实例。     

Optimal lower bounds on the hydrostatic stress amplification inside random two-phase elastic composites

Composites made from two linear isotropic elastic materials are subjected to a uniform hydrostatic stress. It is assumed that only the volume fraction of each elastic material is known. Lower bounds on all rth moments of the hydrostatic stress field inside each phase are obtained for r?2. A lower bound on the maximum value of the hydrostatic stress field is also obtained. These bounds are given by explicit formulas depending on the volume fractions of the constituent materials and their elastic moduli. All of these bounds are shown to be the best possible as they are attained by the hydrostatic stress field inside the Hashin-Shtrikman coated sphere assemblage. The bounds provide a new opportunity for the assessment of load transfer between macroscopic and microscopic scales for statistically defined microstructures.     

Ductile fracture criteria for simulating shear by node separation method

This study is concerned with the mechanics of ductile fracture in bulk metal forming processes by a finite-element analysis and experiments. Developed is a computer program using conventional finite-element method such that the behavior of crack propagation after ductile fracture can be analyzed. The phenomenon of a material separating into two pieces upon shearing and tensile tests has been simulated using the developed computer program. Special attention is focused on the effect of various ductile fracture criteria on crack initiation and propagation during shearing and tensile tests.     

结构拓扑优化研究方法综述

结构拓扑优化研究方法目前有解析方法和数值方法两大类.首先介绍了解析方法中的 Michell理论,它在结构拓扑优化领域研究较早,影响最为深远.随后着重讨论了杆系和连 续体结构拓扑优化的数值方法.杆系结构常采用基结构方法,通过删除部分杆件达到结构 拓扑优化的目的.连续体结构一般要划分为有限单元,通过删除单元形成带孔的连续体, 以实现拓扑优化.介绍了连续体结构拓扑优化常采用的材料模型:各向同性、各向异性和 带微结构材料.并对连续体结构(0-1)拓扑优化中的数值计算不稳定问题的机理进行了分 析,给出了解决方法.此外,对应力约束问题存在解的奇异性现象也作了简要介绍.最后, 对数值方法中的主要数学求解方法进行了简单介绍.     

复合型表面裂纹疲劳门槛应力的估算

表面裂纹是工程构件常见的缺陷，由于实验数据的缺乏及其他困难，断裂力学应用于表面裂纹的疲劳扩展，其经验和成果还十分有限。本文利用复合型断裂准则，对圆棒试样表面小裂纹的门槛应力进行分析和估算，得到了较满意的结果。     

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.     

Convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi-criteria decision making problems

In this paper, we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices, in the context of multi-criteria decision making. We first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts. We consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons, such as the uncertainty level, alternative preference scales and different weight estimation methods. We also consider the case where the comparisons are carried out in a fuzzy manner. It is shown that in most circumstances, augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal. We next address the issue of how this probability can be estimated in practice, from information gathered simply from the comparison matrices of a single expert group. We propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions. The framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome.