Stress Effect Decay Estimates for Anisotropic Material in a Semi-Infinite Strip

对带端面负载的半无限带状各向异性弹性材料建立了Saint-Venant原理。应用能量方法确立了应力效应衰减率的下界,得出了用各向异性材料的弹性常量表示的估计显式。最后,为了说明所得结果,对带端面负载、纤维偏离主轴的石墨-环氧树脂的衰减率给出数值实例。     

带裂缝的双周期各向异性平面弹性基本问题

无限平而中带双周期分布裂缝的弹性基本问题,是有应用价值的重要课题。对于各向同性材料,这个问题业已解决,本文将讨论各向异性的情况。§1.复应力函数设无限各向异性弹性平面中有无限条双周期分布的裂缝,其周期为2w_1,2w_2,不     

各向同性弹性半空间与带孔隙横观各向同性热弹性材料界面上波的传播

在一各向同性弹性半空间上覆盖一层带孔隙的横观各向同性热弹性材料时,研究孔隙对表面波传播的影响.建立"焊接"接触及光滑接触界面条件下的数学模型,导出其频率方程.用图形给出相速度和衰减系数随波数的变化曲线,描述了"焊接"接触界面条件时孔隙和各向异性的影响.得到了"焊接"接触时的单位损耗,以及体积率场、正应力、温度变化的幅值,并对一组特殊模型用图形描述了孔隙和各向异性的影响.研究中还推演出一些特例.     

压电超材料梁中弹性波带隙特性与界面传输的主动控制

该文采用周期压电负电容电路,研究了弹性波超材料梁中带隙特性的主动控制问题.该系统利用外部电路改变所连接压电材料的材料参数,从而改变结构的等效参数,实现对带隙特性的调控.通过对单胞进行控制,可观察到主动控制系统作用时带隙的产生与消失.构造了含有交界面的弹性波超材料梁结构,分析了主动控制系统对波动界面传输特性的影响.     

二维各向异性Boussinesq方程的稳定性

Boussinesq方程是一类在天气预报、海洋生态等领域有广泛应用的地球物理模型,其稳定性研究是流体力学的重要课题之一.本文研究速度场只有水平耗散,温度方程带阻尼项的二维Boussinesq方程在区域T×R上解的稳定性和长时间行为.通过将速度u和温度θ正交分解成水平部分(u,θ)和振荡部分(u,θ),构造恰当的能量泛函并利用各向异性Sobolev不等式及靴带原理证得解的稳定性和衰减率.     

功能梯度板的柱面弯曲弹性力学解

在推广后的England-Spencer功能梯度板理论基础上,研究了功能梯度板在不同荷载作用下的柱面弯曲问题.采用该理论中的位移展开公式,并且材料参数沿板厚方向可以任意连续变化,并将材料由各向同性推广到正交各向异性.假设板在y方向无限长,最终建立了一个从弹性力学理论出发的正交各向异性功能梯度板在横向分布荷载作用下柱面弯曲问题的板理论.通过算例分析,讨论了边界条件、材料梯度及板厚跨比等因素对功能梯度板静力响应的影响.     

混凝土材料裂纹尖端损伤带尺寸特性*

本文采用作者研究各向异性材料裂纹尖端塑性区特性的分析方法,研究了混凝土材料裂纹尖端损伤带尺寸特性.基于单轴应力假定,考虑了混凝土材料的非线性软化特性等影响,提出用两种分析模型:即能量模型和断裂模型来分别讨论.最后,还对这些模型作了比较.     

正交各向异性椭圆板的弹性失稳

本文以von Kármán型方程为基础并利用一般分支理论讨论了正交各向异性椭圆板在面内边缘均布压力作用下的弹性失稳.利用Liapunov-Schmidt过程证明了单特征值处分支解的存在性并利用小摄动展开得到了分支解的渐近表达式.最后利用有限单元法计算了正交各向异性椭圆板的临界载荷并进行了板的过屈曲分析,还考察了材料和几何参数对稳定性的影响.     

无限横观各向同性弹性圆柱中刚性圆盘的扭转振动

分析了无限横观各向同性弹性圆柱中，刚性圆盘的扭转振动问题．绘制的图形显示了材料的各向异性性质对应力强度因子的影响．     

各向异性复合材料的平面周期焊接问题

利用平面弹性复变方法和解析函数边值问题的基本理论,讨论不同材料的各向异性弹性半平面和弹性长条的周期焊接问题,并给出应力分布封闭形式的解。     

各向异性半平面与一各向同性长条的焊接问题

本文利用平面弹性复变方法和解析函数边值问题的基本理论以及积分方程论，研究了各向异性半平面与一各向同性长条的焊接问题，给出了应力分布封闭形式的解。     

The problem of the bending of a beam lying on an elastic base

The plane contact problem of the transmission of a normal force of specified strength onto an elastic anisotropic, wedge-shaped plate by an elastic beam of variable flexural stiffness is considered. The beam is coupled to one of the edges of the plate and its other edge is stress-free. The solution of the problem is obtained in closed form by reducing it to a Karleman boundary-value problem with shear for a strip. A conclusion is reached concerning the nature of the discontinuity of the normal contact stress at the vertex of the wedge.     

Some convexity considerations for a two-dimensional traction problem

Summary A rectangular strip, consisting of homogeneous, isotropic, elastic material, is in an equilibrium state of plane stress, due to actions applied to a pair of opposite edges, the remaining pair being traction-free. The convexity of certain cross-sectional measures of stress is established; and a generalized convexity property is also established for one such measure, leading to an explicit decay estimate for the measure in the case of a semi-infinite strip, one end of which is subjected to a self-equilibrated load.     

DECAY OF ENERGY FOR A DISSIPATIVE ANISOTROPIC ELASTIC SYSTEM

In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua’s estimate technique, we prove the decay property of energy for anisotropic elastic system.     

Bending and torsion of anisotropic thin-walled open sections

A theory of thin-walled open sections, based on Vlasov's assumptions, is proposed. The section is assumed to be composed of rectangular strips whose cross section remains constant in the z-direction. The material is homogeneous and anisotropic with a single plane of elastic symmetry parallel to the middle surface of the strip. The general case of loading-tension, unsymmetrical bending, and constrained torision-is considered.Mekhanika Polimerov, Vol. 3, No. 5, pp. 900–905, 1967     

A Method to Estimate the Inelastic Response in Notched Structures of Anisotropic Materials with Elastic ‐ Perfectly Plastic Behavior

The fatigue strength of engineering structures is often limited by notches which arise from constructive features or manufacturing defects. The constitutive behavior in notch regions is then characterized by small plastic zones which are contained in an elastic region. To avoid costly plastic calculations, approximate methods have been developed to estimate the inelastic stress‐strain response at the notch tip. One of the first and best known approximate models is that of Neuber which, over the last 40 years, has received considerable attention particularly in connection with fatigue life prediction. Numerous studies have been conducted to the verification and the generalization of the Neuber approach which respect to multiaxiality, cyclic loading and creep conditions. Recently an extension of the Neuber method to anisotropic materials has been proposed in [1] and applied to directionally solidified and single crystal Nickel based superalloys as they are used in high temperature material applications. In this short notice we modify the approach in [1] for the special case of an elastic ‐ perfectly plastic anisotropic material.     

Optimization of the stress tensor in an elastic anisotropic half-plane

We consider the problem of optimizing the components of the stress tensor and their integral characteristics. The normal and tangential forces prescribed on the boundary of the elastic anisotropic half-plane y≥0 are chosen from certain function classes of curvilinear strip type. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 110–116.     

A dynamic contact problem which reduces to a singular integral equation with two fixed singularities

The problem of the harmonic sheat oscillations of an elastic strip, coupled to an elastic half-space is considered. Using the method of integral transformations, the problem is reduced to a singular integral equation in the contact stresses in the region where the strip and the half-space are coupled when there are two fixed singularities at points bounding the integration intervals. One of the main results of this paper is the method of solving this equation numerically, taking into account the true singularity of the solution and based on the use of special quadrature formulae for singular integrals. The approximate solution obtained provides the possibility of numerically investigating the effect of the oscillation frequency and the ratio of the elastic constants of the strip and the half-space on the stress distribution in the contact area.     

页岩储层各向异性对水平井坍塌压力的影响

为揭示层理页岩强度各向异性对水平井井壁坍塌压力的影响规律,对取自四川盆地龙马溪组页岩钻井不同层理角度的岩芯,通过岩芯观测、偏光显微镜、扫描电镜试验分别从宏观和微观角度研究了页岩层理特征,并基于单轴抗压强度研究了页岩强度各向异性特征.层理结构发育导致页岩呈现出显著的各向异性特征,粗略地将页岩视为各向同性体及简单采用Mohr-Coulomb准则作为破坏判据,使得预测的维持井壁稳定的坍塌压力不能满足安全钻井的需要.该文在研究层理地层岩石力学特性的基础上,采用横观各向同性地层井周应力分析模型,研究了弹性模量及地应力各向异性比对井周应力的影响;并结合考虑中间主应力的Mogi-Coulomb判据,分析了井壁坍塌压力对弹性模量E和Poisson(泊松)比ν各向异性比值变化的敏感性.实例分析结果表明:弹性模量和水平地应力各向异性比值的变化会对井周应力产生较大影响;Poisson比各向异性对井壁坍塌压力没有明显影响,而弹性模量比值的变化对井壁坍塌压力影响较大;横观各向同性地层中井壁坍塌压力与储层水平和垂直方向的硬脆性强弱关系有关,弹性力学参数各向异性既有可能利于井壁稳定,也可能更易导致井壁的剪切破坏;在实际工程中应根据储层岩石水平和垂直方向的硬脆性强弱关系,确定安全钻井液密度窗口.该结果对现场施工具有很好的指导意义.