自然单元法研究进展

自然单元法是一种基于Voronoi图和Delaunay三角化几何结构,以自然邻点插值为试函数的一种新型数值方法.其既具有无网格方法和经典有限元方法的优点,又克服了两者的一些缺陷,是一种发展前景广阔的求解微分方程的数值方法.自然单元法的形函数满足插值性质,可以像有限元法一样直接施加本质边界条件,不存在基于移动最小二乘拟合的无网格方法不能直接施加本质边界条件的难题.由于自然单元法是无网格方法,可以方便处理有限元方法较难处理的一些问题,例如移动边界和大变形等问题.自然单元法与其他数值方法的最根本区别于其插值格式的不同.将自然邻点插值用于Galerkin过程,就得到基于Voronoi结构的自然单元Galerkin法.自然邻点插值有自然邻点Sibson插值和Laplace插值(非Sibson插值)两种.Laplace插值比Sibson插值在计算上要简单的多,并且不论对凸的或非凸的区域都能精确施加本质边界条件.以Laplace插值为试函数的自然单元法在数值实施上比以Sibson插值为试函数的自然单元法简单.本文对基于Voronoi结构的自然邻点插值和自然单元法的基本思想作了介绍,综述了国内外关于自然单元法的研究成果,总结了自然单元法的优点和尚需解决的问题.      

基于结构动力学的框架结构固有频率估算方法

对框架结构的一阶固有频率与单门框的一阶固有频率的关系进行了推导,找出一种通过部件模态参数估算整体系统的模态参数的方法．通过ANSYS有限元分析对该估算方法进行了验证,并在石油钻机井架底座的有限元模态分析中应用该方法对系统固有频率进行了估计,误差均不超过1％．结论表明,该方法对于框架串联结构的固有频率估算是方便且可行的．     

基于局部搜索算法的自然邻接点方法

自然邻接点方法(NNM)采用自然邻接点形函数进行插值，其插值形函数具有严格定义，且与 有限元形函数一样形式简洁、性能优良，因而避免了EFG法里难以准确施加位移边界条件和 材料不连续条件等诸多主要困难. 但是从形式上看自然邻接点方法仍然属于有网格的方法， 其研究和应用受到了较大的限制. 为了克服这个缺点，对于任意给定的数值积分点，提出了 一种基于局部搜索自然邻接点的寻找算法对NNM进行改进. 改进后的NNM与无单元伽辽金法 (EFG)的插值和求解过程类似，兼具有EFG的真正无网格特性及NNM的便于处理边界和材料 不连续条件等优点. 所得计算结果表明，改进后的NNM的计算精度和计算时间与NNM相当， 是一种比较理想的数值求解方法.     

天然气随动掺氢技术研究进展

氢气是一种零排放的二次能源,是实现“双碳”目标的重要能源之一。采用在役天然气管道或管网输送掺氢天然气,是实现氢气大规模输送的有效方式。精确控制进入输送系统的掺氢比例对系统安全运行具有重要意义。本文介绍了电气式和机械式随动掺氢系统的结构与原理;分析了红外吸收型、热传导型、半导体型浓度传感器和相应的综合测量系统在掺氢比动态调整中的应用;重点评述了目前3个重要在役天然气掺氢示范项目中随动掺氢系统的组成和运行结果;基于工程实践经验展望了天然气掺氢技术的发展趋势。

     

Natural motion density of elastic shells under intensive dynamic loading

The question of the natural motion density in dynamics problems of elastic shells is considered. Motions are studied for which an exponential growth in amplitude with time occurs. The number of natural motions incident in a given range of variation of the exponent is computed by using an idea of R. Courant. The governing natural motions and condensation points at which the natural motion density tends to infinity are found. The condensation points and governing motions are compared in specific examples.     

EMS磁浮列车车/轨耦合系统的分岔现象研究

通过分析EMS磁浮列车系统的Hopf分岔, 研究车轨耦合系统对应的轨道固有频率稳定范围. 采用串级控制悬浮控制器，给出控制器参数与特征频率的关系，在控制器稳定的前提下利用 数值算法计算在系统参数一定、轨道固有频率变化条件下所对应的Hopf分岔点，结合仿真方法 得出轨道固有频率的稳定范围，定性说明了系统载荷、控制器频率、二次系刚度与轨道固有 频率之间的变化关系.     

天然气掺氢管道输运及终端应用

氢能是最有潜力的碳中和清洁能源载体,天然气掺氢在管道输运和终端应用方面具有优势。本文调研了国际上具有代表性的天然气掺氢研究及示范项目,分析了天然气掺氢管道输运和终端应用的可行性和经济性。研究结果表明：低比例的氢气（20%体积比以内）加入天然气管网系统中并不会明显增加相关事故风险及危害,对系统进行轻微改造的情况下最高可以允许50%体积比氢气加入天然气管网系统。通过经济性分析核算了天然气掺氢的成本,给电厂进行天然气掺氢提供参考。鉴于各个国家在天然气成分、管道条件和管道材料上的不同,我国应根据实际的管路、气体具体情况开展对于天然气掺氢的分析研究。

     

基于自然单元法的功能梯度中厚板自由振动分析

自然单元法是一种基于自然邻近插值的无网格数值方法．相对于移动最小二乘近似而言,自然邻近插值不涉及到复杂的矩阵求逆运算,也不需要任何人为的参数．基于一阶剪切变形板理论,利用自然单元法对功能梯度中厚板的自由振动进行了数值分析．功能梯度板材料属性沿厚度方向呈梯度连续变化．由于自然邻近插值函数具有Kronecker delta函数性质,可以直接施加本质边界条件．通过本文给出的方法,对不同梯度指数和不同边界条件的功能梯度中厚板的振动频率进行了计算．通过与文献结果的对比验证了自然单元法求解的有效性．     

黏弹性阻尼作用下轴向运动Timoshenko梁振动特性的研究

黏弹性阻尼一直是轴向运动系统的研究热点之一.以往研究轴向运动系统大都没有考虑黏弹性阻尼的影响.但在工程实际中, 存在黏弹性阻尼的轴向运动体系更为普遍.本文研究了黏弹性阻尼作用下轴向运动Timoshenko梁的振动特性.首先, 采用广义Hamilton原理给出了轴向运动黏弹性Timoshenko梁的动力学方程组和相应的简支边界条件.其次, 应用直接多尺度法得到了轴速和相关参数的对应关系, 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似解析解.最后, 采用微分求积法分析了在有无黏弹性作用下前两阶固有频率和衰减系数随轴速的变化; 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似数值解, 验证了近似解析解的有效性.结果表明: 随着轴速的增大, 梁的固有频率逐渐减小.梁的固有频率和衰减系数随着黏弹性系数的增大而逐渐减小, 其中衰减系数与黏弹性系数成正比关系, 黏弹性系数对第一阶衰减系数和固有频率的影响很小, 对第二阶衰减系数和固有频率的影响较大.      

Frequency analysis of nonlinear free vibration of a cross string

This work concerns nonlinear free vibration of a cross string under large amplitude. The equations governing the nonlinear vibration of the cross string are derived at first from the Hamilton principle, and they take the form of Duffing equation. Then the perturbation method is used to solve the nonlinear coupled natural frequency of the cross string. The nonlinear natural frequency not only has the characteristic of nonlinearity, but also reflects the coupled characteristic, i.e., the natural frequency of the cross string varying with that of its constituent strings. The results show that the overall effect on the cross string is somehow averaged due to the nonlinearity of each constituent string, i.e., the natural frequencies of the cross string contain both the linear natural frequencies of the constituent strings and the nonlinear parts that depend upon the vibration amplitude, the diameter of one constituent string, the length ratio of the two strings, etc., but the contribution of each constituent string to the natural frequency is in different proportions.     

烟塔合一自然通风冷却塔的有限元分析

应用ANSYS有限元软件对浙江省拟建最高烟塔合一冷却塔的内力及线性稳定性进行了分析．计算表明,在72°风向角风压作用下在孔口附近产生局部屈曲,使临界风速急剧下降,而在孔口附近经局部加厚处理可消除局部屈曲现象．     

Free vibrations of shallow nonthin shells with variable thickness and rectangular planform

The free vibrations of shallow orthotropic shells with variable thickness and rectangular planform are studied. The shear strains are taken into account. The spline approximation of unknown functions is used. The natural frequencies are calculated for different boundary conditions. The dependence of the natural frequencies on the curvature of the midsurface is examined. The natural frequencies of shells with constant and variable thickness are compared     

掺氢天然气管道完整性评价技术的进展与挑战

“双碳目标”背景下,我国积极推进掺氢天然气管道发展,本文总结了国内外掺氢天然气管道完整性评价方面的研究进展与挑战,得到主要结论如下。（1）现有金属材料相容性试验结论不明确,亟需制定国际统一的金属材料掺氢相容性试验标准;掺氢后管材、焊缝性能劣化规律不清晰,需系统地开展相关试验,揭示其氢损伤机理。（2）天然气管道非金属密封材料在氢环境中的密封性能及力学性能尚不明确,亟需开展相关试验以探索其性能规律;工程上缺乏高性能的非金属输氢管道,需研发低渗透耐侵蚀的输氢管材。（3）现有无损检测技术对掺氢后天然气管道的适用性研究不足,需改进或研发更高精度的无损检测工具以满足掺氢条件下对缺陷检测精度的要求。（4）掺氢天然气管道缺陷适用性评价方法研究仍处于初级阶段,需要以丰富的试验数据为基础开展耦合考虑氢介质与应力状态的管材微观损伤本构研究,完善掺氢天然气管道缺陷适用性评价方法。本文可为掺氢天然气管道安全保障相关研究提供参考。

     

Vibration analysis of a circular disk tensioned by rolling using finite element method

Summary The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis. Received 18 June 1998; accepted for publication 8 April 1999     

Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases

We study the evolution of characteristics of natural longitudinal vibrations of a circular bar in the case of increasing defect in its cross-section. It is shown that, in the limit case where the defect separates the bar into two independent fragments, the natural frequencies of the initially defect-free bar pass into the natural frequencies of its separate parts. The respective evolution of the natural modes of vibrations is observed. The evolution predicted by the theoretical analysis can be observed experimentally by using the resonance method and constantly increasing the defect till the final separation of the bar into two parts.     

动力弹塑性分析的无网格自然单元法

基于无网格自然单元法,提出了结构动力弹塑性响应分析的一条新途径.自然单元法是一种新兴的无网格数值计算方法,其实质是基于自然邻近插值的伽辽金法.自然单元法在本质边界条件的施加上较采用移动最小二乘法的无网格法具有明显的优势.在空间域上采用自然单元法离散,并运用加权余量法推导了动力弹塑性分析的离散控制方程.然后,采用预校正形式的Newmark法在时间域上进行求解.最后给出了数值算例,并验证了所提方法的有效性和正确性.     

Parametric study of a two degree-of-freedom cylinder subject to vortex-induced vibrations

This numerical work is an attempt to build accurate and continuous response surfaces of two degree-of-freedom vortex-induced vibrations (VIV) of flexibly mounted cylinders for a wide range of transverse and in-line natural frequencies. We consider both the structure and the flow to be two-dimensional. The structure has a low mass damping, with the transverse and in-line mass ratios as well as the transverse and in-line damping coefficients being equal. The goal is to capture the sensitivity of the response to the change in the natural frequencies of the structure. The system is studied for a wide range of transverse natural frequency within the synchronization region. The extent of variation of the in-line natural frequency is chosen to be larger than the one of the transverse natural frequency in order to favor multi-modal responses. No preferred frequencies are emphasized within the intervals of study. The numerical technique uses a multi-element stochastic collocation method coupled to a spectral element based deterministic solver.     

Vibrations of ribbed shallow rectangular shells on an elastic foundation

A procedure to determine the natural frequencies and modes of ribbed shallow shells with rectangular planform on an elastic foundation is developed. The effect of the radius of curvature and the Winkler and Pasternak coefficients of subgrade reaction on the natural frequencies and modes of a shallow spherical shell with a square planform is analyzed. It is revealed that not only the natural frequencies but also the modes of the shell depend on the coefficients of subgrade reaction     

The application of ideas associated with materials with memory to modeling the inelastic behavior of solid bodies

In this paper, we present a new way to describe the rate-independent inelastic behavior of metals undergoing finite deformations. Experiments indicate that the stress often has a stronger dependence on the inelastic history in the more recent past as compared to that in the distant past. For this reason, an “annihilation” function is used to weight the inelastic history so that less importance is given to the strains in the more distant past. This “annihilation” function does not depend explicitly on time, but instead on the pathlength associated with the history of stress-free or natural configurations in the strain space relative to the current natural configuration. In this formulation the current configuration is adopted as the reference configuration for the kinematic quantities. The constitutive equation for stress is expressed in terms of the strain associated with the current natural configuration relative to the current actual configuration. Equations have been developed to prescribe the change in the natural configuration as the material yields. A general yield function has been defined in terms of the relative natural strain to restrict the manner in which the natural configuration changes. Since the yield conditions are in terms of the relative natural strain, we can account for situations in which a material yields during the process of unloading. For the sake of simplicity, the elastic properties of the material are considered to be constant throughout the deformation with the material remaining isotropic with respect to the natural configuration. With the proposed theory, we have examined the “Bauschinger effect” which is exhibited by metals that are deformed beyond the yield limit before being deformed beyond the yield limit in the reverse direction.     

磁场对铁磁结构动态特性的影响

研究了两种铁磁材料结构(板梁和圆柱壳)在不同的磁场下固有频率的变化。频谱分析仪产生的扫频正弦信号通过压电陶瓷片对试件进行激励;压电薄膜作为感知元件再把感知信号送回频谱分析仪。根据共振原理,从频谱分析仪的频率响应曲线可以得到试件的各阶固有频率。通过改变外加磁场的大小,用同样的方法可以得到不同磁场下的固有频率。实验结果表明,铁磁板梁固有频率的变化很大程度上依赖于所施加磁场的方向:当磁场顺着板梁的长度方向时,板梁的固有频率会随着外加磁场的增大而增大;然而当磁场施加在板梁的厚度方向时,固有频率是先降低然后再升高。对铁磁材料圆柱壳,当磁场顺着圆柱壳的轴线方向增大时固有频率是逐渐增大然后达到一个饱和值。