二维八次对称准晶的断裂动力学问题

基于准晶弹性流体动力学模型,采用有限差分法研究了含Griffith裂纹八次对称准晶在不同冲击载荷下的动态响应,得到了应力、位移和应力强度因子的数值结果,讨论了不同冲击载荷对动力学行为的影响.     

分数阶热弹理论下重力场对二维纤维增强介质的影响

基于Sherief等提出的分数阶广义热弹性耦合理论，研究了在热冲击作用下二维纤维增强弹性体的热弹性问题.考虑了重力对二维纤维增强线性热弹性各向同性介质的影响，建立了控制方程.运用正则模态法，经过数值计算，对控制方程进行求解，得到了不同分数阶参数和不同重力场下无量纲温度、位移和应力分量的表达式，以图形的方式展示了变量的分布规律并对结果展开了讨论.研究结果为:重力场和分数阶参数对纤维增强介质的位移及应力有着重要的影响，但对温度的影响有限.     

基于有限变形弹塑性模型模拟伪弹性合金全程变形行为

提出一个J2流的有限弹塑性本构方程来显式、全面地模拟了形状记忆合金(SMAs)在3个不同阶段加载并卸载所表现出来的应力-对数应变关系.这3个阶段包括变形完全恢复的伪弹性阶段、变形部分恢复的塑性阶段以及软化破坏阶段.该文的主要思想在于从实验数据的形函数出发,得到用形函数表达的多轴硬化函数,进而代入到本构方程,建立一个能模拟任意形状应力-对数应变关系,多轴有效的本构方程.该文方法的优势在于避免考虑微观到宏观的平均方法、相变条件等一系列复杂处理,大大减少了计算量.所得到的数值结果可以精确匹配实验数据.     

加性二值噪声激励下Duffing系统的随机分岔

研究了Duffing系统在加性二值噪声作用下的随机分岔现象.首先,根据二值噪声的统计特性,推导得到二值噪声状态间的跃迁概率,据此对二值噪声进行了数值模拟.其次,利用四阶Runge-Kutta(龙格-库塔)数值算法得到该系统位移和速率的稳态联合概率密度及位移的稳态概率密度.然后,通过对位移稳态概率密度单双峰结构变化的研究,发现加性二值噪声的状态和强度能够诱导系统产生随机分岔现象.最后,观察到随着系统非对称参数的逐渐变化,系统同样产生了随机分岔现象.     

模糊数学在岩心钻探工程上的应用

国内外地质勘探部门在对岩石分级的研究中,多只限于岩石可钻性的研究,提出了各种岩石按可钻性分级的方案.这种分级仅考虑岩石机械破碎的难易程度,而未考虑地层复杂、孔壁稳定、钻孔弯曲、采心难易等因素对钻探工艺全过程的影响.所以,这种分级虽然可以反映岩石的可钻性,却总不能全面反映矿区岩心钻探的难易程度.当管理部门要对矿区勘探的投资进行估算时,就必须综合地评价钻探的难易程度.这时,我们认为不仅要考虑可钻性因素,还要考虑稳定性、采心性和孔斜性的因素.从四性     

考虑不同破坏形式下隧道锚承载力及破坏阶段研究

现有研究多以锚岩接触面出现塑性区域或应力峰值点转移作为达到极限状态的判别标准,但不同工程地质情况会导致隧道锚(TTA)破裂面线形存在较大差异,很难准确推导出隧道锚的极限承载力.为了进一步探求隧道锚在拉拔荷载下的工作过程,得到更加明确的隧道锚极限承载力的表达形式,采用幂指数函数形式表征倒锥形破坏破裂面的线形,基于Mindlin应力解与峰值剪应力控制理论得到界面破坏应力分布形式,推导了界面破坏与倒锥台破坏形式下的承载能力公式;采用国内5座悬索桥隧道锚承载力进行算例验证,同时分析研究了不同参数对隧道锚极限承载力的影响.研究表明：两种破坏形式下,承载力的主要来源为破裂面的黏结力,占总承载力的50%以上,承载力均随着长度与内聚力的增加而线性增加;承载力随着倾斜角的增加而增加,但增长速度减慢,界面破坏形式下出现先增加后减小的现象.对比以往试验以及数值模拟结果,与该文推导结果基本一致,分析公式计算结果和位移增长曲线,发现隧道锚工作过程明显呈现3个阶段,最终破坏形式为界面破坏和倒锥形破坏两种破坏模式的结合.     

蠕变损伤材料中缺口尖端稳定扩展的应力场

研究了在拉伸载荷和反平面载荷作用下蠕变损伤材料缺口尖端稳定扩展的应力场．假设材料的应力及位移势函数,得到了缺口尖端场的各参数分量,进而在小范围蠕变条件下,建立了缺口尖端稳定扩展的蠕变损伤控制方程,并考虑缺口尖端蠕变钝化作用和问题的边界条件,对控制方程进行了数值分析,得到了缺口尖端的应力场,并讨论了缺口尖端应力场随各影响参数的变化规律．结果表明,缺口尖端的应力具有r1/(1-n)的奇异性,应力率具有rn/(1-n)的奇异性,n是蠕变指数．     

加载和卸载过程中复合材料叠层圆柱曲板后屈曲路径的研究

本文用动态松弛法研究了在加载和卸载过程中复合材料叠层圆柱曲板的后屈曲路径,发现了加载路径与卸载路径不重合的现象,给出了在均匀单轴压力作用下的十字叠层圆柱曲板在两种边界条件下的数值结果,并讨论了层数、曲率半径、初始几何缺陷等因素对后屈曲路径的影响.     

混凝土轴拉加卸载随机损伤模型的建立与试验验证

为了分析及深入探讨混凝土在受拉加载及卸载情况下的力学特性,基于随机损伤本构关系提出了一种混凝土轴拉加卸载模型,推导出了混凝土加卸载的应力 应变关系表达式.为了印证理论表达式,进行了混凝土轴向拉伸及加卸载的试验研究,测得了混凝土的材料参数及其相应的轴拉加卸载应力-应变曲线.结合模型的计算结果,对混凝土的轴拉加卸载试验结果进行了对比分析,结果表明:混凝土轴拉加卸载模型能够预测混凝土的极限强度,同时能描述混凝土的强度软化、加载过程中的弹模折减及卸载后的塑性变形.     

粘弹层合板的自由振动和横向应力

基于Reddy分层理论并在板厚方向取二次位移插值函数来推导出粘弹层合板的动力学方程,得到了简支粘弹夹层层合板的振动频率,其数值与已知文献数据吻合较好,且能够计算出协调的横向应力.在低频自由振动时,横向剪应力是造成粘弹层合板脱层的主要原因;高频时,横向正应力在脱层破坏中起主要作用.分析了粘弹材料模量对层合板横向应力的影响以及横向应力最大值与面内应力最大值的比值.结果表明所采用的算法、算式及所编写的程序是可靠的.     

Structural damage accumulation and stable postcritical deformation of composite materials

The macroscopic failure of composite materials is preceded by complex multilevel processes accompanied by accumulation and localization of damaged centers and formation of a failure cluster. Therefore, the study of these mechanisms is one of the basic problems for the mechanics of modern composite materials used in aerospace engineering. The formation of a theory of the stable postcritical deformation of the work-softening media is considered. The pseudo-plastic deformation affected by structural damage of granular composites is investigated within the framework of the considered two-level structurally phenomenological model of heterogeneous media. The stable evolution of the interconnected processes is accompanied by stress redistributions, partial or complete unloading, and strain or damage localization that are one of the main causes of implementation of the postcritical deformation stage. The numerical calculation results of inelastic deformation and failure of the periodic unidirectional fiber-reinforced composites are presented under conditions of the displacement-controlled transverse proportional loading mode. The main mechanisms of the work-softening behavior for the indicated type of materials are described in the macro-homogeneous stress-strain states. Macroscopically, the failure of heterogeneous media as a result of postcritical deformation and the loss of stability of damage accumulation depends on the stiffness of the loading system. When a deformable body is fixed on the closed surface with sufficiently but not infinitely large coefficients of stiffness, it is possible to observe the equilibrium development of the localized volumes of work-softening and damage. The constitutive equations for the work-softening isotropic, transverse isotropic, and orthotropic media are presented. The effect of the loading system on the stability of deformation, damage accumulation, and failure under monotone and nonmonotone triaxial loading was studied. The growth of failure strains with increase in stiffness of the loading system and unequal resistance of heterogeneous body are registered and investigated. A preventive unloading method is offered for the mathematical modeling of the damage accumulation during the testing of the materials on the servo-controlled systems. The displacement-controlled mode is simulated by a series of soft loading and unloading cycles. The detected phenomenon of failure where the unloading leads to stress-strain diagrams with a negative slope of the descending branch was not found either in the displacement or stress-controlled monotone loading mode.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 234–250, March–April, 1998.     

Axisymmetric torsional fretting contact between a spherical punch and an FGPM coating

The axisymmetric torsional fretting contact between a rigid conducting spherical punch and a functionally graded piezoelectric material (FGPM) coating is studied in this paper. The exponential model is used to simulate the inhomogeneous electro-mechanical properties of the FGPMs coating. The conducting spherical punch with a constant surface electric potential is considered in the contact. A normal force and a cyclic torque are applied to the two contact bodies. The applied torque produces an outer annular slip area and an inner stick area. The torsion angle is produced within the inner stick area as a rigid body. With the aid of the Hankel integral transform technique, we can reduce the contact problem to the singular integral equations of the Cauchy type. Then the unknown electro-mechanical fields and stick/slip area can be obtained numerically. The effect of the gradient index on the surface electro-mechanical fields is discussed at loading and unloading phases. The Mises stress and principal stress at the contact surface are also discussed to predict the possible location of fretting damage and failure.     

Stress and deformation states in the annulus made from shape memory material

The contribution deals with the stress and deformation states in an annulus made of shape memory material (SMM). The loading‐unloading process is going on at constant temperature, which is below temperature M_f (martensite finish temperature). The research is focused on the determination of the stress and deformation states in the annulus after loading and unloading process. These results are necessary for treating process of constrained recovery in shape memory annulus. The real loading‐unloading function in the stress‐strain coordinate system of shape memory material (Ni–Ti–Cu) is included in the mathematical model.     

非热平衡Schwarzschild-de Sitter黑洞的熵

从Schwarzschild—de Sitter时空背景下的K1ein—Gordon方程出发，利用brick—wall方法计算了黑洞的自由能和熵．这种黑洞由于存在两个视界面，而且它们的温度不相同，因此用一般方法计算熵存在着一定的困难．采用改进的brick—wall模型，认为自由能和熵主要来自于视界附近薄层的贡献，很好地解决了这一困难，并得到了满意的结果．结果表明，这种黑洞的熵为它的两个视界面积之和的1／4，与人们预期的结果相符．由此可见，渐近de Sitter时空中的黑洞摘除了黑洞视界面的贡献之外，还应包括宇宙视界面的贡献．这从一定程度上指示了黑洞熵与视界面积之间的内在联系，也更进一步地指示了brick—wall模型的本质．     

流固耦合作用下狭窄颈动脉内非Newton血流分析

采用计算流体力学方法分别对6种狭窄率的颈动脉内非Newton瞬态血流进行流固耦合数值分析.研究了狭窄率对颈动脉内血流动力学分布的影响,以探索狭窄率与颈动脉内粥样斑块形成的关系.结果表明,狭窄率不同的颈动脉内血流动力学分布特性明显不同,与0.05,0.1,0.2,0.3和04这5种狭窄率的颈动脉内血流动力学分布特性相比,狭窄率为0.5的颈动脉内血流动力学分布独特,狭窄部位附近区域存在面积较大的低速涡流区;复杂血流作用下,该区域分布低壁面压力,异常壁面切应力,较大管壁形变量和von Mises应力;血流速度低使血液中脂质、纤维蛋白等大分子易沉积,低壁面压力引起的明显“负压”效应引发脑部供血障碍,异常壁面切应力作用下粥样斑块易破裂与脱落,并堵塞脑血管,较大的von Mises应力易引起应力集中,导致血管破裂,为脑卒中发生提供有利条件.因此,狭窄率越大对颈动脉内血流动力学分布的影响越显著,促进颈动脉粥样斑块形成与发展,并引发缺血性脑卒中.     

A constitutive model for thermoplastic materials subjected to high strain rates

Reliable prediction of the behaviour of structures made from polymers is a topic under considerable investigation in engineering practice. Especially, if the structure is subjected to dynamic loading, constitutive models considering the mechanical behaviour properly are not available in commercial finite element codes yet. A constitutive model is derived including important phenomena like necking, strain rate dependency, unloading behaviour and damage. In particular, different yield surfaces in compression and tension and strain rate dependent failure, the latter with damage induced erosion, is taken into account. With the present formulation, standard verification tests can be simulated successfully. Also, an elastic damage model can be used to approximate the unloading behaviour of thermoplastics adequately. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于博弈论视角的稀土矿区环境治理及监管策略研究

针对稀土矿区环境治理的复杂性,本文通过建立地方政府和稀土企业之间的动态演化博弈模型,分析了博弈双方在不同情形下的演化稳定策略及其影响因素,并利用matlab对其进行数值仿真。研究表明,地方政府的监管成本、执行环境规制时对稀土企业的奖惩政策、稀土企业的治污成本以及非法开采时的额外收益都会影响地方政府与稀土企业的演化稳定策略,降低地方政府的监管成本、稀土企业的治污成本等都会引导博弈双方的演化稳定策略趋向于{严格监管,合法开采},从而促进矿区环境的可持续性发展。     

基于博弈论视角的稀土矿区环境治理及监管策略研究

针对稀土矿区环境治理的复杂性,本文通过建立地方政府和稀土企业之间的动态演化博弈模型,分析了博弈双方在不同情形下的演化稳定策略及其影响因素,并利用matlab对其进行数值仿真。研究表明,地方政府的监管成本、执行环境规制时对稀土企业的奖惩政策、稀土企业的治污成本以及非法开采时的额外收益都会影响地方政府与稀土企业的演化稳定策略,降低地方政府的监管成本、稀土企业的治污成本等都会引导博弈双方的演化稳定策略趋向于{严格监管,合法开采},从而促进矿区环境的可持续性发展。     

Relation between the vectors Э and S for a plastic material with a sequence of ray-like loading paths

Two different complex loading paths are investigated in stress space — longitudinal tension with subsequent total unloading and reloading in transverse tension or compression. For these loading paths the local strains theory [4] is used to determine the values of the components of the strain vector {₁, ₂} in five-dimensional space for nonlinearities n=3 and n=5 together with the components of the stress vector S{S₁, S₂}. A relation between the vectors and S is established in terms of the given loading parameter k.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 241–245, March–April, 1970.