混凝土断裂过程的力学模型与数值模拟

混凝土是一种典型的非均匀准脆性材料，其断裂过程是非常复杂的. 评述了混凝土断裂以及断裂过程研究的进展状况，主要总结了一些研究混凝 土断裂的宏观力学方法和模型，介绍了从混凝土的细观层次出发模拟其断裂 过程的数值模型.最后，简单介绍了作者用细观数值方法模拟混凝土宏观断 裂过程的研究成果.  

混凝土断裂尺寸效应的研究进展

混凝土结构断裂破坏的尺寸效应问题是近几十年来一个十分重要的研究领域．本文分析了混凝土断裂参数产生尺寸效应的原因，讨论了断裂过程区的测试方法，对国内外提出的一些尺寸效应的分析方法进行了评述．在此基础上对混凝土断裂尺寸效应的研究提出了自己的看法  

直接增强自然单元法计算应力强度因子

自然单元法是一种新兴的无网格数值计算方法,但应用于裂纹问题计算时,其近似函数并不能准确反映裂纹尖端渐进应力场的奇异性,为获得足够的计算精度,需要在缝尖附近增大结点的布置密度。针对裂纹问题提出一种增强的自然单元法,将缝尖渐近位移场函数嵌入到自然单元法近似函数中,给出了增强试函数的构造方法,推导了总体刚度矩阵和荷载列阵的相关列式。应力强度因子可以作为附加未知量直接算得,也可用J积分或相互作用能量积分方法进行计算,对增强区域的选择和影响进行了分析。算例结果表明,基于增强自然单元法采用围线积分方法计算应力强度因子具有很高的精度,但直接以附加结点自由度形式计算则精度有所降低。  

多波前并行处理的弹塑性子结构并行有限元

研究一种基于ＰＶＭ的弹塑性子结构并行有限元法。利用多个波前，对各子结构并行地进行静凝聚。再采用预条件共轭梯度法（ＰＣＧ）并行求解界面方程。算例表明该方法能获得较好的并行加速比，同时也能有癣地节省内存量。  

基本解方法与边界节点法求解Helmholtz方程的比较研究

基本解方法和边界节点法是基于径向基函数的两种重要无网格边界离散数值技术。针对Helmholtz方程,本文比较研究这两种数值方法在不同计算区域问题上的计算精度、插值矩阵对称性、病态性及计算成本。数值试验结果表明,两种方法都可以有效求解边界数据准确的Helmholtz问题。在数值离散过程中,两种方法都可以通过调整配置点的位置减少插值矩阵的条件数;用边界节点法求解产生的插值矩阵是对称的,而基本解方法的插值矩阵不对称;边界节点法所需的计算时间比基本解方法略小,同时只需要后者一半的内存空间。  

沉桩挤土位移应力变分解和积分泛函收敛性分析

静压桩是一种挤土桩，沉桩挤土作用将引发很多工程问题. 实际的贯桩过程发生在半无限成 层土体中，且单桩具有空间轴对称性，桩的形状和长度也各不相同，因此需要研究半无限土 体中一般桩孔扩张的特性和解. 通过对沉桩挤土的研究现状和实际存在问题的分析，建立 沉桩挤土三维模型、设定符合变分约束条件的位移函数. 根据研究区域的积分泛函得到问题 的位移和应力解. 由于能量泛函涉及三维广义积分问题，所以重点对积分和 解的收敛性进行了分析，并应用经典土压力理论、小孔扩张理论和Ansys计算结果 对计算和分析结果进行验证.  

Time Rates of Hill's Strain Tensors

Based on Hill's principal components formulae, two kinds of basis-free time rate formulae for Hill's strain tensors are proposed in this paper, which are obtained for the cases of distinct stretches, double coalescence and triple coalescence. Furthermore, relations between the coefficients in the representation for the strain tensor and its time derivative are disclosed. This revised version was published online in August 2006 with corrections to the Cover Date.  

一种XFEM断裂分析的裂尖单元新型改进函数

提出了一种适用于裂尖改进单元的新型改进函数, 基于三角变换的方法, 保留裂纹尖端场的应力奇异性和裂纹上、下表面的位移不连续性, 将常规扩展有限元法裂尖改进单元的4 项改进函数缩减为2 项, 裂尖改进单元的结点由常规的8 个改进自由度减少为4 个. 采用2 个正交的水平集函数表征材料内部裂纹面, 详细阐述了改进单元类型的判别方法, 给出一种改进单元的分区域积分方案. 最后, 若干断裂力学问题经典算例的数值计算结果表明:建议的裂尖改进函数具有较高的数值精度, 该方法是十分有效的.  

Interval finite element method and its application on anti-slide stability analysis

The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.  

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.