弹性力学平衡微分方程推导方法的改进

一些经典的工科《弹性力学》教材推导平衡微分方程的过程在数学上不够严密.利用多元函数偏导数的定义和积分中值定理给出了逻辑严密的推导.     

弹性压应力波下直杆动力失稳的机理和判据

基于应力波理论和失稳瞬间能量的转换和守恒,导出了一个直杆动力分岔失稳的准则:(1)直杆在发生分岔失稳的瞬间所释放出的压缩变形能等于屈曲所需变形能与屈曲动能之和;(2)在上述能量转换过程中,能量对时间的变化率服从守恒定律.应用临界条件(1)推导出的直杆动力失稳的控制方程和杆端边界条件以及连续条件,与应用哈密顿原理推导的结果完全相同,但不足以构成求解直杆动力失稳问题的完备定解条件.应用临界条件(2)导出压缩波前的附加约束方程.由此得出该问题的完备定解条件,导出包含两个特征参数的一对特征方程.从而建立了求解直杆动力失稳模态和两个特征参数(临界力参数和失稳惯性项指数参数即动力特征参数)的较严密理论方法.     

速度瞬心加速度的简单求法

现有文献中推导平面运动刚体瞬心加速度的公式,存在推理不严密或过程繁琐的问题.本文应用点的复合运动、刚体的复合运动和自然坐标系中点的加速度公式求瞬心加速度,推导过程较简明.     

关于点的合成运动速度合成定理两种推导的辨析

针对И.М.伏龙科夫著的理论力学教材中点的合成运动速度合成定理推导，指出推导过程在概念上和数学上出现的错 误. 并给出正确的推导过程，以引起力学教学工作者注意.     

推导加速度合成公式的“牵连点跟踪法”

 在理论力学课程中关于点的合成运动的教学,可采用跟踪"牵连点" 的方式来推导(加) 速度合成定理. 即让某瞬时的牵连点与动点从空间位置上"分离",从定系和动系的原点,同时向动点和牵连点各引出两条矢径,跟踪牵连点任意时刻的运动. 然后将以上引出的四条矢径所满足的基本关系式对时间求导,即得到任意时刻的(加) 速度关系式. 再将牵连点的条件代入该(加) 速度关系式,可导出(加) 速度合成定理. 该推导方法概念明确、清晰,各物理量间具有较好的"可辨识性",便于学生理解和掌握.     

流体动反力公式的应用范围及其推广

<正> 一般的理论力学教材在推导出流体流过弯管时的动反力公式后,往往给出图1所示的一个习题作为(1)式的一个应用.我们认为,直接套用(1)式求解图1中的问题是不妥当的.因为从(1)式的推导过程可以看出,(1)式只适用于只有一个进口及一个出口的流动.由于图1     

光束穿越不同介质时LDV的测试及其误差分析

本文应用平面几何及光学原理,从理论和实践上分析了应用激光多普勒测速仪(LDV)进行实际测量时,在有窗口的情况下应该注意的几个问题,并给出了测量点位置偏差修正的定量公式以及光轴方向上测速精度相对误差的评估方程,省略了繁琐的理论推导.     

推导柯尼希定理和平行轴定理的一种新方法

 针对定点运动刚体,利用动量定理、对固定点和质心的动量矩定理推导了柯尼希定理; 针对平面运动刚体,利用动量定理和对动点的动量矩定理,推导了平行轴定理. 给出与以 往教材不同的推导方法,并从两个方面推广了文献的结果. 从不同角度进行理论推导,可以 帮助我们理解物理量、物理定律(定理)之间的联系,提高对物理本质的认识水平.     

非均匀异性线弹性广义平面问题的一种变换模型

本文是对文献建立的平面边值问题一个应力函数变量理论的一种推广,并补充了些完善性的内容.虽然这个问题的均匀情况曾由文献得到复数解,但在边值处理上及所用方法上不如本文的严密与完整.1.基本模型及广义变分原理符号:二维问题σ_(ij)、τ_i(=σ_(3i))为应力,u_i、ω为位移,上划“—”为给定值.f_i、f_3为体力,α_(ijkl)等为柔性系数.定义于平面域σ、边界C,边界法、切线单位向量n_i、s_i.用直角坐标系张量表示,并下角“,n”、“,s”为对边界法、切线微商.     

Euler坐标系与Lagrange坐标系下激波条件的比较

从多方气体Naiver-Stokes(N-S)方程出发,通过行波解存在的条件,推导Euler坐标系下激波的Rankine-Hugoniot(R-H)条件及熵条件,并证明这与Lagrange坐标系下的条件一致.     

中国西南山区第四纪冰川堆积物工程地质分类探讨

中国的大陆冰川堆积物几乎都属于巨粒土或块石（漂石）土、碎石土,但因复杂的物质组成和组构特征,各地或同一地区不同成因类型（冰碛、冰水）的堆积物具有极为不同的工程地质性质,其地质体稳定性和地质灾害的易发性存在着显著的差异。我国已有的工程分类框架不能满足当代冰川堆积物甚至其他碎石土（巨粒土）的工程地质和地质灾害研究的需要。中国西南山区冰川堆积物的物质成分、细观结构等的野外调查和室内测试分析结果表明,冰川堆积物的物质成分和组构特征主要表现为：颗粒组成的不均一性和多元性、组构单元的双元性、结构的无序性和胶结性等。冰川堆积物的物质成分和组构特征与其工程性质具有密切的关系,是冰川堆积物工程地质分类的基础。本文探讨了中国西南山区冰川堆积物的工程地质分类问题,提出基于胶结程度和粒度组成的二级分类方案,对冰川堆积物及其他块（漂）石土的工程地质研究和工程实践具有一定指导意义。     

3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Summary  The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces. Received 28 February 2001; accepted for publication 26 June 2001     

Forced response of quadratic nonlinear oscillator: comparison of various approaches

The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches. The forced vibration of snap-through mechanism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincaré method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are compared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method predicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the LindstedtPoincaré method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.     

2009年6·5重庆武隆鸡尾山崩滑灾害基本特征与成因机理初步研究

2009年6月5日下午15时许,重庆市武隆县铁矿乡鸡尾山山体发生了大规模的崩滑,约500万m3被结构面切割成“积木块”状的灰岩山体,沿缓倾页岩软弱夹层发生整体滑动。高速运动的滑体物质在堵塞前部宽约200m,深约50m的铁匠沟沟谷后,形成平均厚约30m,纵向长度约2200m的堆积区,掩埋了12户民房和正在开采铁矿的矿井入口,造成10人死亡,64人失踪,8人受伤,成为近年来少有的一次崩滑灾难性事件。本文在对灾害现场进行大量地质调查的基础上,结合遥感、三维激光扫描等综合手段,对鸡尾山崩滑体特征进行了详细描述,对灾害发生原因进行了初步分析。结果表明,鸡尾山山体垮塌是在不利的地质结构条件下,并受到长期重力、岩溶等作用和采矿活动的影响,因前部起阻挡作用的关键块体被剪断突破而导致的一起大型山体崩滑事件。深入研究鸡尾山崩滑体的形成条件和成灾机理,对我国西南地区存在与鸡尾山崩滑体类似地质条件的灾害隐患点的减灾防灾工作,具有重要的指导意义。     

An efficient method for solving the mixed direct-inverse problem of the transonic rotational flow in plane casades

The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse problem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks. The calculations have been carried out on the DPS-8 computer, and for the direct problem, only 50–80 iterations are needed, and 50–80 seconds of CPU time are required.     

Design,fabrication, testing and mechanical analysis of bulk-micromachined flowmeters

Micromachined piezoresistive flowmeters with four different types of sensing structures have been designed, fabricated and tested. Piezoresistors were defined at the end of the sensors through p-diffusion, and their values were about 3.5 kΩ Wheatstone bridge was configured with the piezoresistors in order to measure the output response. The output voltage increases with increasing flow rate of air, obeying determined relationships. The testing results show that the sensors that are designed for measuring 10L/M in full operational range have desired sensitivities. The sensor chip is manufactured with bulk-micromachining technologies, requiring a set of seven masks.     

Pansystems studies in stability,bifurcation and chaos

This paper divides fixed subsets into three kinds, mainly discusses the existence of II-type fixed subset, connects the investigations infixed subsets with the studies in non-linear problems, such as stability, bifurcation, chaos, etc., and proposes a kind of discrete simulation to Liapunov stability and his second method.     

Fatigue crack-tip deformation,crack growth and life prediction in polycarbonate

Low-cycle fatigue fracture of polycarbonate is investigated. Local strain in the vicinity of the notch root and crack tip has been measured in real time by using a fine-grid method. The relationships among the local strain, crack initiation from the notch root and crack propagation of the crack tip are studied, and a method for more precise life estimation is suggested. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

自重体积力作用下坡体张应力及坡面位移的变化规律

为了提高对边坡体力学行为的认识,借助于FLAC有限差分软件的数值模拟,并结和相似理论的推导验证,研究了在仅有自重体积力作用的条件下,线弹性边坡体的一些力学特征及其与相关变量或物理力学参数的相关关系。没有外载荷影响时边坡地表最大主应力和最小主应力分别平行和垂直于地表,当深度增加时,主应力的取向逐渐变成竖直和水平两个方向,坡面处既有张应力区也有拉应力区,坡脚处亦存在较大的张应力,这是自重体积力作用下边坡体应力分布的一般性特征,在本文和前人的研究中都能体现。本文还重点揭露了：坡角线性增加时坡顶最大张应力的变化速率表现为：快——慢——快; 沿坡顶面竖直向下张应力随深度增加线性减小; 小变形条件下边坡应力场与弹性模量无关; 最后验证了满足相似理论的坡体,坡面对应点的位移比是其几何尺寸比的平方倍。本文不仅是对既有研究成果的进一步补充,而且为以后研究复杂条件下边坡体的力学特征奠定了基础,对于理论和实践都有一定的启发意义。     

基于中间构形的大变形弹塑性模型

在大变形弹塑性本构理论中,一个基本的问题是弹性变形和塑性变形的分解.通常采用两种分解方式,一是将变形率(或应变率)加法分解为弹性和塑性两部分,其中,弹性变形率与Kirchhoff应力的客观率通过弹性张量联系起来构成所谓的次弹性模型,而塑性变形率与Kirchhoff应力使用流动法则建立联系;另一种是基于中间构形将变形梯度进行乘法分解,它假定通过虚拟的卸载过程得到一个无应力的中间构形,建立所谓超弹性-塑性模型.研究了基于变形梯度乘法分解并且基于中间构形的大变形弹塑性模型所具有的若干性质,包括:在不同的构形上,塑性旋率的存在性、背应力的对称性、塑性变形率与屈服面的正交性以及它们之间的关系.首先,使用张量函数表示理论,建立了各向同性函数的若干特殊性质,并导出了张量的张量值函数在中间构形到当前构形之间进行前推后拉的简单关系式.然后,基于这些特殊性质和关系式,从热力学定律出发,建立模型在不同构形上的数学表达,包括客观率表示的率形式和连续切向刚度等,从而获得模型所具有的若干性质.最后,将模型与4种其他模型进行了比较分析.