突变理论在浅埋煤层组合关键层中的应用

 应用突变理论的方法，对组合关键层的力学模型进行了分析， 导出了系统的总势能函数表达式, 并建立了尖角型突变模型.定量地 分析了顶板的台阶下沉量以及组合关键层失稳的充要条件，得出的 结论有实际意义.     

对裂纹扩展规律Paris公式物理本质的探讨

首先讨论了著名力学家K.Krausz和A.S.Krausz关于Paris公式物理本质研究的成果，从材料的微观结构和裂纹尖端的应力场出发，应用位错动力学理论，热激活能理论和速率过程理论对疲劳裂纹扩展规律进行了微观到宏观的探讨。最终推导出疲劳裂纹扩展速率的一个解析表示式，该式严格地定了Paris公式的两个试验常数，赋予了Paris公式明确的物理意义，从而真实地揭示了Paris公式的物理本质，为这一经验的普遍规律奠定了理论基础。     

脆性岩石蠕变裂纹成核宏细观力学机理研究

脆性岩石内部细观裂纹扩展、贯通及成核影响下的脆性蠕变行为, 对深部地下工程围岩微震及岩爆事件评价有着重要意义. 然而, 目前能够解释裂纹成核损伤突变影响下, 脆性岩石完整蠕变宏细观力学机理模型的研究很少. 本文基于脆性岩石亚临界裂纹扩展模型、裂纹-应变-声发射事件相关的损伤模型及裂纹成核损伤时间演化路径函数, 提出了一种脆性岩石裂纹成核损伤突变影响下的蠕变宏细观力学模型. 裂纹成核损伤时间演化路径函数通过岩石内部裂纹成核损伤突变大小$\Delta D_{CN}$及相邻裂纹成核损伤时间差$\Delta t$进行定义, 该函数可以结合岩石声发射监测试验数据定义的岩石损伤数据确定. 通过与试验结果对比分析验证模型的合理性. 并讨论了裂纹成核损伤大小、相邻裂纹成核损伤时间间隔、及裂纹成核数量对脆性岩蠕变裂纹长度、裂纹速率、轴向应变及应变率的影响. 该结果对于更加合理、经济、高效的深部地下工程施工及设计提供了一定的理论支持.      

弹性T项对裂尖参数和裂纹扩展路径稳定性的作用

研究了弹性T项在主裂纹与近裂尖微空洞干涉问题中对裂尖参数和裂纹扩展路径稳定性的影响作用.利用“伪力”法,并通过解决主裂纹与近裂尖微空洞干涉问题,对远场纯1型载荷和远场弹性T项载荷下,该干涉问题中弹性T项的影响作用进行了分析从数值结果可以看出：由于空洞的存在;释放了弹性T项所引起的应力,弹性T项对裂尖参数;应力强度因子和J积分都有直接显著的影响,因而,它对该载荷下的裂纹扩展路径的稳定性有控制作用。     

土质边坡失稳的突变性分析

对土质边坡圆弧滑动稳定性问题，采用应力软化模型，由系统能量导出极限平衡方程，运用突变理论方法对土坡失稳进行了分析。分析表明，边坡参数变化为某一临界值时，土坡的滑动位移突然增大，发生突变失稳现象，由刚体极限平衡稳定理论无法体现应力软化土质边坡的这种失稳的突变性。     

The activation method for discretized conservative nonlinear stability problems with multiple parameter and state variables

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables,the activation method is put forward,by which activated potential functions and activated equilibrium equations are derived.The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory.It is more generalized and more normalized than conventional perturbation methods.The activated potential functions may be transformed into normalized catastrophe potential functions.The activated equilibrium equations may be treated as bifurcation equations.The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory.     

应用突变理论分析Euler压杆的稳定性

建立了Euler压杆问题的能量表达式。对此模型，应用突变理论进行稳定分析，得出了系统全部的分叉集与突变流形。突变流形为一族层层嵌套、互不交叉的抛物线。分析的结论要比有限差分法、有限单元法、大范围非线形分析等数值计算的结果简洁、明了，有助于压杆后屈曲问题的研究。     

突变理论在工程地质中的应用

本文说明了突变理论应用于工程地质中的一般方法。着重通过实例介绍尖点突变理论在工程地质中的应用现状,其中包括用突变理论评价层状结构斜坡、地下洞室的顶板冒落及活断层的稳定性,以及斜坡失稳的时间预报等问题。同时对其应用前景作了展望。     

光滑试样表面疲劳裂纹演化的数值仿真

考虑裂纹形核，扩展，合并以及晶界的作用等因素，对光滑圆试样表面疲劳裂纹的演化进行了数值模拟。结果表明，疲劳裂纹系统的演化是由无序向有序转化的过程，演化诱致突变。这一过程与实验观察到的结果一致。疲劳裂纹系统的演化终态具有很大的分散性，主要表现为裂纹路径的随机性和突变寿命的分散性。样本的随机性是造成上述分散性的外因，系统对裂纹位形的敏感性是内因。     

弹性圆柱壳冲击扭转屈曲的突变模型

本文将突变理论用于处理冲击载荷下弹性结构的屈曲问题,文中建立了结构冲击屈曲的突变准则,认为临界阶跃载荷位于所提出突变系统的分叉集之中,并由此对两端固支的弹性圆柱壳扭转屈曲进行了分析,给出了不同初缺陷时的临界阶跃扭矩计算公式,通过对临界静态扭矩的计算,表明临界阶跃扭矩小于临界静态扭矩.     

三点弯曲试样幂硬化材料裂纹撕裂扩展的实验研究

本文应用三点弯曲试样和撕裂模量理论对弹塑性裂纹撕裂扩展的稳定性进行了实验研究,得出了适用于三点弯曲试样的施加撕裂模量T_(app)的计算公式。结果说明了材料硬化和系统柔度等因素对裂纹扩展稳定性的影响。实验中采用多层高柔度组合梁系统,得到了随加载系统柔度增加,裂纹扩展从慢稳定到失稳发展的过程。证明了撕裂模量理论的有效性。实验结果与理论预测相符。     

Atomistic simulation study on the crack growth stability of graphene under uniaxial tension and indentation

Meccanica - Combining a series of atomistic simulations with fracture mechanics theory, we systematically investigate the crack growth stability of graphene under tension and indentation, with a...     

Effects of humidity and temperature on subcritical crack growth in sandstone

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. The influences of the surrounding environmental conditions and rock fabric on subcritical crack growth in sedimentary rocks in air are yet to be clarified, while the nature of subcritical crack growth in igneous rocks has been studied well. In this study, the influences of temperature and relative humidity on subcritical crack growth in Berea sandstone, Shirahama sandstone and Kushiro sandstone were investigated in air. The load relaxation method of Double Torsion (DT) testing method was used to measure both crack velocity and stress intensity factor under a controlled temperature and relative humidity.Results show that the change of the crack velocity at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. On the other hand, we show that the crack velocity increased by several orders of magnitude when the relative humidity increased threefold or fourfold under a constant temperature at a given stress intensity factor. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. It is therefore necessary to consider the additional mechanisms for subcritical crack growth in sandstone. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in sandstone in air is affected remarkably by the relative humidity and the amount of clays in rock.     

The stability of growth of a through-wall circumferential crack in a pipe subject to combined bending and tensile loadings

The stability of growth of a through-wall circumferential crack in a pipe is analysed for the case where the material has a high crack growth resistance, the analysis being based on the tearing modulus procedure. Rotations and lateral displacements are applied at the ends of the pipe, and this allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The general conclusion is that tensile loadings can have an adverse effect on crack stability, in accord with the conclusion reached in the author's earlier studies of plane strain crack growth in a beam. The stability results are compared with those obtained by Tada, Paris and Gamble, who allowed the tensile loadings to affect the position of the neutral axis, but did not consider instability in terms of the deformations produced by these loadings.     

A catastrophic model for vibrational buckling of elastic arches

This paper represents an attempt at the application of catastrophe theory to thedynamic stability of engineering structures.The authors not only obtain a catastrophicmodel of vibrational buckling of elastic arches,but also give the critical condition of losingstability.     

The stability of crack growth in a beam subject to combined bending and tensile loadings. II: Beam subject to rotations and lateral displacements at the ends

The stability of crack growth in a beam subject to combined bending and tensile loadings is examined for the case where the material is very ductile and where the beam is built-in at one end. Application of a displacement at the free end, and variation of the angle which the displacement makes with the beam, allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The stability analysis is based on the tearing modulus procedure, and the general conclusion is that tensile loadings can promote crack instability.     

Experimental analysis of crack propagation stability in single edge notch specimens

An experimental technique for analyzing the crack propagation stability of single edge notch specimen is discussed. The testing rig and its calibration procedure are described. Analyzed are the crack path under biaxial loading and its correlation with theoretical predictions. The mode II influence on the crack path is also presented. Use is made of the computer program ANGCRK. Fracture criteria are applied to determine the stability of crack growth. Stability is assumed to prevail when the second term of the eigenfunction series expansion is negative. Otherwise, the crack growth could be unstable.     

The stability of crack growth in a beam subject to combined bending and tensile loadings: I: Beam built-in at one end

The stability of crack growth in a beam subject to combined bending and tensile loadings is examined for the case where the material is very ductile and where the beam is built-in at one end. Application of a displacement at the free end, and variation of the angle which the displacement makes with the beam, allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The stability analysis is based on the tearing modulus procedure, and the general conclusion is that tensile loadings can promote crack instability.     

静力预加载结构冲击屈曲的突变模型

基于突变理论给出静力预加载弹性结构冲击屈曲的准则,并将其用于处理Budian-sky-Hutchinson简单力学模型的冲击屈曲分析和受扭圆柱壳的冲击扭转屈曲分析,给出了临界载荷的求解公式。     

CAVITATED BIFURCATION FOR INCOMPRESSIBLE HYPERELASTIC MATERIAL

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