动态断裂理论和实验研究进展

本文介绍和评述了动态断裂力学在理论和实验研究方面的现有进展,特别是近年来对材料非线性和动态效应对裂纹扩展及其稳定性的影响的研究以及实验测试技术的现状和问题的研究,并对今后的研究方向提出了作者的看法.     

压电层合板热屈曲问题的精确分析

本文在作者们以前工作的基础上导出了热压电介弹性稳定性问题的控制微分方程，提出了热压电层合板热屈曲问题的数学和学解法。由于最后所得特征值问题的复杂性，热屈曲临界必须数值求解。文中对不同压电材非压电材料层构成的层合板作了具体计算，考虑了压电性对屈曲温度的影响。     

稳定性分析数值方法综述

本文综述了流体动力学稳定性分析中所使用过的数值方法,每种方法都通过文献中举出的一个典型例子作了说明。努力了解近代稳定性计算中所采用的各种数值方法,并汇总在附录Ⅱ中。对与无粘问题有关的各种困难作了解释。还讨论了Navier-Stokes方程作为初值问题的直接解法。      

层电层合板柱形屈曲

导出了压电介质弹性稳定性问题的控制微分方程，提出了压电层板柱形屈曲的数学弹性力学解法，由于最后所得特征值问题的复杂性，屈曲临界载荷必须数值求解。文中对不同压电材料的双层板作了具体计算，考查了压电性对屈曲载荷的影响。     

压电层合板柱形屈曲

导出了压电介质弹性稳定性问题的控制微分方程，提出了压电层合板柱形屈曲的数学弹性力学解法．由于最后所得特征值问题的复杂性，屈曲临界载荷必须数值求解．文中对不同压电材料的双层极作了具体计算，考查了压电性对屈曲载荷的影响．     

各向异性层状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质位移位，应力传播矩阵，给出了直角坐标系各向异性层状介质中弹性波的传播矩阵解法，该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题，数值结果表明，计算效率，准确性及稳定性均较好。     

各向异性展状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质内位移、应力传递矩阵，给出了直角坐标系下各向异性层状介质中弹性波的传播矩阵解法．该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题．数值结果表明，计算效率、准确性及稳定性均较好．     

双材料界面裂纹的改进广义有限差分法

采用数值方法进行断裂力学分析时,裂纹尖端奇异区域处理的好坏直接关系到最终断裂力学参数的求解精度。与传统均匀介质不同,复合材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性,许多用于表征经典的平方根和负平方根物理场渐近性的传统方法也因此失效。论文提出了一种改进的广义有限差分法,该方法基于多元函数泰勒级数展开和移动最小二乘法的思想,将节点变量的各阶导数由相邻点集函数的加权线性累加来近似,具有无网格、无数值积分、数据准备简单、稀疏矩阵快速求解等优点。为提高该方法求解断裂力学问题的计算精度和数值稳定性,论文引入了裂尖奇异区域局部点簇的自动创建技术和一种基于局部点簇几何尺寸的矩阵正则化算法。数值算例表明,所提算法稳定,效率高,在不增加计算量的前提下,显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性。     

陷落腔的流场数值计算研究

本文对有限分析解法的近似计算方法及其对计算精度的影响进行了数值计算和分析讨论；然后采用有限分析解法，对前、后壁壁缘高度不同的三种腔内流场运动发展过程及腔口剪切层运动情况作了数值计算，得到的腔口剪切层上腔口随边相互作用情况与对应腔的流场显示实验结果进行了比较，两者一致，计算结果表明，采用本文发展的近似方法计算可靠，可以较大地提高计算效率。     

流体力学中的差分方法 Ⅰ.二维涡度方程的数值解

本文以二维涡度方程为例,系统地讨论了流体力学差分方程的理论问题.文中按照守恒律和传输律构造了许多格式,介绍了广义稳定性,严格估计了周期解问题的误差,分析了初一边值问题中边界形状、边界条件及其处理方式和边值误差对计算的稳定性的影响,又根据守恒律处理了无粘流及大梯度解的计算问题,最后,研究了定常流计算格式的解的存在性和动态松弛法的收敛性.文中的全部结果都是严格证明的,所采用的方法对一般流体问题也是适用的.文中还举例说明了这些结果在空气动力学计算和数值天气预报中的应用.     

页岩水力压裂的关键力学问题

页岩气是指以吸附和游离时而还有流体相的形态状态赋存于泥页岩中的非常规天然气。页岩气开采成为我国绿色能源开发的新领域。尽管北美页岩气革命取得了成功,但目前仍仅有预期产量5~15%的油气采收率,问题出在什么地方？水力压裂被认为是提高采收率的关键一环,但水力压裂过程中复杂缝网的形成和力学控制机理尚不清楚,这给力学家提出了巨大的挑战和机遇。结合本课题组近期研究成果,本文从理论、计算和实验三个方面对页岩水力压裂中的关键基础力学问题进行介绍和总结。主要内容包括发展页岩人工裂缝扩展的大型物理模型实验,建立页岩本构模型和断裂力学理论,发展耦合断裂力学和流体力学的裂缝网扩展数值模拟方法。页岩水力压裂研究对发展断裂力学的实验技术、理论模型和数值模拟方法起到推动作用,对提高我国页岩气高效开采技术具有重要意义。     

Solution of nonstationary problems in the mechanics of anisotropic bodies by the method of dynamic photoelasticity

The results obtained in developing and applying the method of dynamic photoelasticity to two-dimensional problems in the mechanics of anisotropic bodies are reviewed. The theory behind the method and its engineering implementation are described. The capabilities of the method are illustrated by solving specific nonstationary problems: dynamic stress concentration, diffraction of longitudinal and transverse waves by free and reinforced holes, dynamic fracture of orthotropic plates with holes and cracks under impulsive and explosive loads     

弹性与断裂力学复变方法研究进展——纪念弹性与断裂力学复变函数法提出100周年

1909年,俄国数学力学家哥洛索夫首先将复变函数方法应用于二维弹性力学问题,揭开了弹性力学复变方法研究的序幕.100年来,复变方法在求解弹性与断裂力学问题中取得了很大发展,特别在断裂力学中的应用尤为成功.2009年恰逢弹性力学复变方法提出100周年,该文试图总结100年来复变方法在经典断裂力学、复合材料断裂力学、新型材料断裂力学以及三维空间断裂问题中的发展与应用,以作纪念.     

无网格MPM法三维前处理系统设计

无网格法在解决爆炸冲击、裂纹扩展、高速碰撞以及大变形等问题时,由于与网格无关,能够避免有限元法因网格畸变计算精度降低或计算终止的矛盾,是目前求解固体力学问题的有效方法之一,也是近年来研究的热点。前处理对于无网格法数值计算是非常重要的环节,基于面向对象程序设计思想,应用C 和OpenGL开发了三维图形交互方式的MPM法前处理系统,提出了应用递归四叉树法、扫描表示法和CSG法划分任意形状非等间距的MPM法质点单元,为建立通用的无网格前处理平台提出了有效的解决方案。     

On the uses of special crack tip elements in numerical rock fracture mechanics

Numerical methods such as boundary element methods are widely used for the stress analysis in solid mechanics. These methods are also used for crack analysis in rock fracture mechanics. There are singularities for the stresses and displacements at the crack tips in fracture mechanics problem, which decrease the accuracy of the numerical results in areas very close to the crack ends. To overcome this, higher order elements and isoperimetric higher order elements have been used. Recently, special crack tip elements have been proposed and used in most of the numerical fracture mechanics models. These elements can drastically increase the accuracy of the results near the crack tips, but in most of the models only one special crack tip element has been used for each crack end. In this study the uses of higher order crack tip elements are discussed and a higher order displacement discontinuity method is used to investigate the effect of these elements on the accuracy of the results in some crack problems. The useful shape functions for two special crack tip elements, are derived and given in the text and appendix for both infinite and semi-infinite plane problems. In this analysis both Mode I and Mode II stress intensity factors are computed . Some example problems are solved and the computed results are compared with the results given in the literature. The numerical results obtained here are in good agreement with those cited in the literature. For the curved crack problem, the strain energy release rate, G can be calculated accurately in the vicinity of the crack tips by using the higher order displacement discontinuity method with a quadratic variation of displacement discontinuity elements and with two special crack tip elements at each crack end.     

分析薄壳塑性动力响应问题的一种数值方法

探索薄壳塑性动力响应问题的分析与数值方法,是当今力学中的重要课题之一。笔者曾给出联合应用拉普拉斯变换和最小二乘法分析梁、板、壳塑性动力响应的方法。本文分别针对承受中载的短壳和长壳问题,给出只用最小二乘法分析其塑性动力响应的方法。     

功能梯度材料裂纹尖端动态应力场

研究受反平面剪切作用的功能梯度材料动态裂纹问题,通过积分变换-对偶积分方程方法推出了裂纹尖端动态应力场,时间域内的动态应力强度因子由Laplace数值反演获得,研究结果表明功能梯度材料的梯度越大,相应的裂纹问题的动态应力强度因子值越低。     

近场动力学方法及其应用

近场动力学(peridynamics,PD)是一种新兴的基于非局部作用思想建立模型并通过求解空间积分方程描述物质力学行为的方法.它兼有分子动力学方法和无网格方法的优点,避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性,又突破了经典分子动力学方法在计算尺度上的局限,在宏/微观不连续力学问题分析中均表现出很高的求解精度和效率.首先概述了PD方法的理论基础、建模思路和计算体系;进而介绍了PD方法在不同尺度不连续力学问题中的应用,包括均匀与非均匀材料和结构的大变形、损伤、断裂、冲击、穿透和失稳问题,结晶相变动力学问题以及纳米材料和结构的破坏问题;最后讨论了PD方法在理论、计算和应用等方面值得进一步研究的问题.     

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.The project supported by the National Natural Science Foundation of China (50579081) and the Australian Research Council (DP0452681)The English text was polished by Keren Wang.     

An introduction to dynamic photoelasticity

The general area of elastodynamics is divided into four more limited topics including, stress-wave propagation, vibration and impact, fracture propagation and quasi-static transients. The application of dynamic photoelasticity to each topic is discussed. Recording methods used in dynamic photoelasticity which are reviewed include the high-speed framing camera, the Cranz-Schardin system, Q-switched ruby lasers, and a stopaction strobe system. Advantages and disadvantages of each method of recording are covered. Analysis procedures used in interpreting the dynamic isochromatic-fringe patterns are described. Examples are illustrated where separation of the principal stresses is possible and a calibration method for determining the dynamic material-fringe valuef _σ ^* is reviewed. Finally, four applications of dynamic photoelasticity to problems arising in geophysics, fracture mechanics, flaw detection and mining are briefly reviewed to show the versatility of the dynamic photoelastic method are described.