地下开采过程损伤场演化与地表变形的时变分析

以形状随时间变化的物体——时变体为研究对象，将损伤理论与时变力学结合，引入与时变过程相关的损伤参数，形成损伤时变力学分析方法。针对岩石介质特性给出了弹性损伤时变力学本构方程，并利用虚功原理建立相应数值化方法和分析过程。利用损伤时变力学分析方法对某地下煤层开采过程进行计算机仿真分析，给出形状时变引起的损伤场与地表移动的动态演化过程，并对比了非时变以及施工分析结果。研究表明，损伤时变分析可得到连续变化的位移及损伤演化图，相比非时变的常规分析和施工分析能更好地模拟连续施工，为工程施工分析与预测提供更加科学和有效的手段。为实现开采过程的经济和安全，应该采用损伤时变力学的分析方法。     

工程施工路径相关性的数值仿真

本文将损伤理论与时变力学耦联,形成用于模似施工的损伤时变力学方法,文中推导了基本方程和数值化算式。利用时变分析法对某地下煤层开采过程进行计算机仿真分析,给出了三种不同路径下开采引起地表沉陷的时空演化图,并进行对比分析。对体现出的位移、损伤与施工路径相关现象进行了探讨,并定量给出损伤时变分析下不同开采路径造成的最终力学状态的差别。本文中损伤时变力学方法为施工过程分析提供了一种新方法与手段。     

岩体施工过程损伤演化预测的时变力学分析

由建立的岩体损伤本构模型，依据时变力学理论对岩体进行不同施工路径下的分步开挖计算，并对施工过程中各点损伤演化历程进行计算机仿真模拟，以预测后续开挖的损伤状态及寻求较优施工步序。理论及算例分析均表明：存在损伤演化时，不同施工步序下岩体终应力位移和损伤状态均不同，设计与施工应进行损伤演化的时变力学分析，以保证施工安全。     

?????????乤?????

本文阐述时变力学这一新的研究方向,对其基本课题、特征及力学、数学方法与进展作了较为系统概述,并结合工程实践说明时变固体力学方向研究的重要性与发展前景．     

飞行器变后掠过程非定常气动特性形成机理

可变体飞行器变后掠过程中的时变气动力与力矩特性对于飞行安全具有重要意义,是亟待深入研究的基础问题.通过风洞实验对其开展了研究,揭示了可变体飞行器变后掠引起的气动特性动态迟滞现象及滞回环大小与方向的影响因素.基于风洞实验结果和力学中一些重要概念,提出了3种物理效应:流场迟滞效应、附加运动效应、固壁牵连效应,以此定性与定量论证了可变体飞行器变后掠过程中非定常气动特性的形成机理.除了能解释实验现象,这一机理研究亦可用于后续可变体飞行器变后掠过程中的气动特性建模.     

无限粘弹性平面中孔洞扩展的时变力学解析解

从粘弹性时变力学基本方程出发,针对Maxwell本构模型,导出了双向等压下粘弹性平面中圆孔半径任意规律扩展时的时变力学解析解.在内径线性时变时,其结果与用对应原理法得出的解相同,其解的可靠性得到验证.与对应原理法相比,文中的结果适用于半径任意时变情况,更具一般性.     

混凝土材料损伤-自愈行为的湿化力多场耦合分析

荷载与环境共同工作下的混凝土损伤-愈合力学行为具有典型的内在湿化力多场耦合特征．本文以混凝土中CaCO3 沉淀自愈机制为例,建立了一种湿-化-力多场耦合分析模型．通过引入一组扩散和化学反应方程,对材料微观结构层次的物理化学过程进行数学建模．随后,基于连续损伤愈合力学理论,将自愈效应引入混凝土损伤本构关系,发展出混凝土湿化力耦合分析模型并进行模型验证．针对单轴拉伸混凝土试样进行多场耦合数值分析,考察了关键参数对愈合过程的作用规律以及自愈进程对混凝土材料力学行为的影响．本文的研究为混凝土在运行环境下的损伤-愈合行为以及性能演变提供了定量分析方法．     

地下洞室开挖过程中洞周损伤分布的时变反演

洞室开挖过程中，洞周围岩的损伤场是时间和空间的函数。本文由建立的岩体时变损伤本构模型，基于位移反演理论，依据各步开挖后洞周及深部测线量测位移，对地下洞室由开挖引起的时变损伤分布情况进行辨识。通过构造损伤分布拟合函数直接反演洞周损伤分布的时变过程，尝试了用拟合函数法实现动态分布参数的反分析。在对某直墙半园拱顶隧道进行反演时，将洞室边界映射成单位圆，建立了由衰减函数和傅立叶级数构成的拟合函数，并采用约束优化法反演。最终结果显示，反演得到的区域损伤平均值与真值相比，绝大多数误差较小。本文法在地下工程施工的岩体内部损伤监测中具有一定的参考价值。     

时变固体力学的黏弹性解

基于时变力学的对应性原理,建立一种黏弹性时变力学的一般性解法,适用于一类时变力学问题的求解。     

分数维空间中的损伤力学研究初探

结合损伤力学和分形几何理论，给出分数维空间中分形损伤变量定义ω（ｄ，ζ）及其解析表达式．指出欧氏空间损伤变量ω０实际是分数维空间分形损伤变量ω（ｄ，ζ）当维数取Ｅｕｃｌｉｄｅａｎ维数时的一种特例，将欧氏空间损伤变量定义推广到分数维空间，建立起一种兼顾反映损伤细观结构效应和宏观损伤力学分析需要的损伤定义与描述方法．在此基础上，推导了材料损伤演化律和损伤本构关系的分形表达形式．作为例证，文中分析了单调压缩载荷下混凝土损伤及演化行为．实验对比分析表明：分形损伤模型较好地反映了混凝土实际损伤力学行为．     

A study of linear time-varying systems

Some linear time-varying systems that can be solved in closed form and are of practical importance in the problems of mechanics are considered. Several properties of the linear time-varying systems whose matrices belong to different classes simultaneously are studied. The stability analysis is performed using a nontraditional method of matrix decomposition. A number of mechanical problems are discussed to illustrate the efficiency of the proposed method.     

基于非齐次复合Poisson过程的正交异性钢桥面板细节疲劳裂纹随机扩展研究

传统的正交异性钢桥面板疲劳损伤评估常采用确定性和可靠性分析方法,忽略了疲劳裂纹扩展的随机性影响,针对这一问题,提出钢桥面板细节疲劳随机扩展分析方法。本文以南溪长江大桥为工程背景,基于长期车辆荷载监测数据,建立了车辆荷载非齐次复合Poisson过程模型。建立钢桥面板有限元模型,采用瞬态分析方法将随机车辆荷载转化成细节疲劳应力,基于线弹性断裂力学理论推导U肋-顶板焊接细节疲劳裂纹扩展时变微分方程,实现宏观关系式疲劳应力幅次数-疲劳损伤至微观表达式应力时间序列-疲劳损伤转换,讨论了车载次序及超载对疲劳裂纹扩展的影响。研究结果表明,非齐次复合泊松过程模型能够较好描述随机车流运营状态,车辆荷载的次序对疲劳裂纹扩展速率的影响不可忽略,重车排序靠前时能够促使疲劳裂纹扩展增速,南溪长江大桥细节点的车辆超载迟滞效应修正系数取值0.804。     

Bi-variable damage model for fatigue life prediction of metal components

Based on the theory of continuum damage mechanics,a bi-variable damage mechanics model is developed,which,according to thermodynamics,is accessible to derivation of damage driving force,damage evolution equation and damage evolution criteria. Furthermore,damage evolution equations of time rate are established by the generalized Drucker’s postulate. The damage evolution equation of cycle rate is obtained by integrating the time damage evolution equations,and the fatigue life prediction method for smooth specimens under repeated loading with constant strain amplitude is constructed. Likewise,for notched specimens under the repeated loading with constant strain amplitude,the fatigue life prediction method is obtained on the ground of the theory of conservative integral in damage mechanics. Thus,the material parameters in the damage evolution equation can be obtained by reference to the fatigue test results of standard specimens with stress concentration factor equal to 1,2 and 3.     

Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

单轴拉伸条件下脆性岩石微裂纹损伤模型研究

利用断裂力学、损伤力学和均匀化原理,对脆性岩石单轴拉伸条件下的力学特性进行分析,建立了脆性岩石的微裂纹损伤本构模型.首先对岩石内部微裂纹的统计分布规律进行分析,给出了理论分析过程中微裂纹分布的假设条件,在此基础上,参考已有研究成果,得到含细长微裂纹脆性岩石有效弹性参数的计算公式.然后,对岩石内部单一微裂纹进行断裂力学和损伤力学分析,得到了扩展裂纹尖端的应力强度因子计算公式,在一定微裂纹断裂扩展准则和断裂扩展速率的假设基础上,利用积分原理,得到了岩石整体的损伤变量和损伤演化方程,由此建立单轴拉伸条件下脆性岩石的微裂纹损伤本构模型.最后,通过一花岗岩的单轴拉伸试验结果对微裂纹损伤本构模型进行了验证.     

弹脆性材料的损伤本构关系及应用

本文根据连续损伤力学方法,对弹脆性材料损伤的力学响应进行一般分析。理论分析中,材料与损伤都是各向异性的。还导出了计算损伤张量、有效弹性张量、真实应力张量以及损伤能耗率张量的实用表达式。     

Investigation of the damage variable basic issues in continuum damage and healing mechanics

Consistent mathematics and mechanics are used here to properly interpret the damage variable within the confines of the concept of reduced area due to damage. In this work basic issues are investigated for the damage variable in conjunction with continuum damage and healing mechanics. First, the issue of the additive decomposition of the damage variable into damage due to voids and damage due to cracks in continuum damage mechanics is discussed. The accurate decomposition is shown to be non-additive and involves a term due to the interaction of cracks and voids. It is shown also that the additive decomposition can only be used for the special case of small damage. Furthermore, a new decomposition is derived for the evolution of the damage variable. The second issue to be discussed is the new concept of independent and dependent damage processes. For this purpose, exact expressions for the two types of damage processes are presented. The third issue addressed is the concept of healing processes occurring in series and in parallel. In this regard, systematically and consistently, the equations of healing processes occurring either consecutively or simultaneously are discussed. This is followed by introducing the new concept of small healing in damaged materials. Simplified equations that apply when healing effects are small are shown. Finally, some interesting and special damage processes using a systematic and original formulation are presented.     

高速电梯系统时变动力学模型与分析

以往关于电梯系统的研究指出，引起电梯系统振动的主要原因在于外部激励－由曳引机，承重装置，拖动和控制系统等引起。这是基于经典的结构共振理论得出的结论，但不能解释某些电梯的振动行为。本文从时变结构力学的观点出发，计及电梯曳引钢丝绳的长度随时间变化，建立起电梯系统的变刚度动力学模型，采用解析方法给出了高速电梯弹性振动的位移和加速度响应表达式。从理论上证明作为时变系统的电梯，具有振荡运动的特征，存在由变刚度引起的自激振动。进一步研究表明，电梯提速意味着曳引钢丝绳的初始扰动增大，导致电梯振动的加速度也增大，对电梯的舒适性有负面影响。     

Sufficient conditions of the various stabilities of the linear time-varying delayed differential equations

Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative, Lozinskii measure and the generalized scalar Halanay delayed differential inequality. They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions' space is infinite-dimensional. Then some sufficient conditions of the stability, asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative. It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.