含多裂纹损伤圆弧曲梁自由振动扰动的有限元网格自适应分析

该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实施微裂纹损伤诱发截面弱化,实现多裂纹深度、位置、数目的模拟。引入变截面Timoshenko梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁自由振动问题,得到优化的网格和满足预设误差限的高精度自振频率和振型解答,研究多裂纹损伤对圆弧曲梁振型的扰动行为。数值算例表明,该算法中网格非均匀加密可适应裂纹损伤引起的振型变化,应用于各类曲梁夹角和裂纹损伤分布工况下的自由振动研究,定量分析了多裂纹损伤深度、数目、分布对圆弧曲梁自振频率和振型的扰动影响,检验了该文算法的精确性和实用性。     

曲梁弯扭屈曲分析

本文基于有限变形理论导出了薄壁曲梁位移和应变的一般表达式。从探讨薄壁曲梁弯扭屈曲的变形模态出发,考虑其弯矩作用平面内变形的影响,利用变分原理导出了曲梁稳定分析的基本微分方程。稳定分析表明,即使绕弱轴弯曲,曲梁也可能发生弯扭屈曲。对于曲率甚小的情况,本文把曲梁看作为具有初曲率的直梁,较精确地分析了初曲率对直梁弯扭屈曲临界弯矩的影响。此外,本文给出的闭合解与Timoshenko,Vlasov及Chai Hong Yoo等人的结果进行了比较,指出了其间差异的根源所在。     

脉冲载荷下裂纹损伤梁的动力屈曲

研究含初始缺陷裂纹梁一端固定，另一端被一质量块沿轴向以某一速度进行碰撞而导致的动力屈出问题。根据Hamilton原理导出考虑初始缺陷及横向剪切变形时裂纹梁的动力屈曲控制方程，并应用线弹簧理论将裂纹引入到屈曲控制方程中，用有限差分法对控制方程进行求解，基于B-R动力屈曲判断准则，确定临界冲击速度。比较了裂纹梁与无裂纹梁的临界冲击速度和屈曲模态，针对裂纹梁主要考察了不同的冲击块质量、初挠度形状等因素对屈曲模态的影响。     

变截面变曲率梁振型的有限元超收敛拼片恢复解和网格自适应分析

该文提出变截面变曲率梁振型的有限元后处理超收敛拼片恢复方法,建立各阶振型的超收敛解,并基于振型超收敛解进行变截面曲梁面内和面外自由振动的自适应分析。在位移型有限元后处理阶段,引入超收敛拼片恢复方法和高阶形函数插值技术,得到振型(位移)的超收敛解。利用振型超收敛解估计当前网格下振型有限元解的能量模形式下的误差,并指导网格进行自适应细分加密分析,获得优化的网格和满足预设误差限的高精度解答。数值算例表明该算法适于求解不同曲线形态、多类边界条件、变截面、变曲率形式的曲梁面内和面外自由振动连续阶频率和振型,解答精确、分析过程高效可靠。     

基于屈曲模态的弹性压弯构件平面内二阶弯矩计算

目前,对于一般情形,结构工程师缺乏简便可靠的手段计算钢结构构件的二阶效应,采用大挠度大变形的直接分析法成为唯一选择.该文从一般情形的等截面等轴力压弯构件平面内受力的基本方程出发,证明了其屈曲模态的正交性以及各种可能平衡状态的稳定性,并首次采用屈曲模态分解法,得到了构件二阶效应的屈曲模态级数解.更进一步,结合构件屈曲荷载...     

基于摄动法的多条裂纹欧拉梁特征模态分析

基于摄动理论推导了带多条开口裂纹的欧拉梁的特征模态参数的理论计算公式。采用最直接的方式将梁开口裂纹模拟成梁微段内的横截面折减并用δ函数表达了带开口裂纹的梁沿轴线的截面惯矩和线质量等物理参数。基于此,建立了裂纹梁动力微分方程,并采用一阶摄动理论推导得到了梁的模态频率和振型计算公式。简支梁及悬臂梁算例研究表明,该方法具有很好的精度,与有限元模拟结果及实验结果都能很好地吻合。并采用此方法分析了裂纹深度和位置对带多条开口裂纹梁的特征模态参数的影响。结果表明,裂纹对各阶模态频率虽然影响有限,但其引起的各阶频率变化有着明显的模式,可用于结构损伤定位;裂纹对模态振型影响不明显,但对模态曲率影响比较大,可用于结构损伤位置和程度的诊断。     

基于模态频率的缺口梁疲劳裂纹扩展寿命预测

从试验出发,研究了含V型缺口悬臂梁在循环载荷作用下的疲劳裂纹扩展特性及其模态频率变化规律,分析了模态频率与裂纹扩展增量间的关联性。将裂纹扩展增量作为损伤参量,建立了基于模态频率下降率与损伤参量的关系。基于损伤力学,建立了裂纹损伤与循环加载次数的演化模型。结合模态频率下降率与裂纹损伤参量的关系,提出了一种基于模态频率下降率的缺口梁疲劳裂纹扩展寿命预测方法,实现了基于当前裂纹损伤和对应循环次数的疲劳裂纹扩展剩余寿命预测。结果表明,模态频率下降率对缺口梁的疲劳裂纹扩展寿命敏感,该方法预测的疲劳裂纹扩展寿命与实测的疲劳裂纹扩展寿命基本吻合。     

轴心受压梭形变截面钢管格构柱的弹性屈曲性能

梭形钢管格构柱是由若干钢管分肢以及许多横向缀管组成的变截面轴心受压构件,良好的力学特性和优美的建筑造型使其广泛应用于索膜结构、大跨度空间结构及高层结构的支承体系,它是近年来出现的一种新型的结构构件。利用有限元软件ANSYS分析了梭形三肢钢管格构柱的几何参数对其弹性屈曲荷载和屈曲模态的影响。这些几何参数包括:柱长、整体长细比、分肢钢管几何尺寸(外径和壁厚)、横向缀管几何尺寸(外径和壁厚)、横向缀管数量(或分肢长细比)等。分析结果表明,梭形格构柱在不同的结构参数下的屈曲荷载和屈曲模态与等截面柱有很大的不同,其中“S”形的屈曲模态反映了这种构件新的屈曲性能。     

含多条裂纹变截面简支梁的自由振动

基于传递矩阵方法,提出了一种求解含多条裂纹变截面简支梁固有频率的新方法。针对一类可推导振型函数的变截面梁结构,采用无质量弯曲弹簧来等效梁结构上的横向裂纹,推导出含变截面参数和裂纹几何参数的整段变截面梁传递矩阵;根据简支梁的边界条件,得到含裂纹变截面简支梁的特征传递矩阵,研究变截面参数、裂纹条数和裂纹几何参数对变截面简支梁固有频率的影响。结果表明:裂纹对变截面梁模态的影响非常大,会显著降低变截面简支梁的各阶固有频率。     

折线形开口薄壁截面圆弧曲梁弯扭理论

现有薄壁曲梁弯扭理论缺乏严密的理论推导。本文基于薄壁构件理论的两个基本假设，精确地导出了任意折线形开口薄壁截面圆弧曲梁的翘曲位移、正应力、剪应力及其各自合力的精确表示式。为便于应用，本文也给出了槽形截面（分槽口向里和向外）曲梁和Π形截面曲梁的简化公式     

含裂纹功能梯度Euler-Bernoulli梁和Timoshenko梁的屈曲载荷计算与分析

含裂纹构件的屈曲载荷是结构是否安全的判定准则之一, 其计算与分析也是结构健康监测和安全评价中关注的重要问题。基于Euler-Bernoulli梁理论和Timoshenko梁理论, 建立了一种求解含裂纹功能梯度材料梁的屈曲载荷计算方法。首先裂纹导致的构件截面转角不连续性由转动弹簧模型进行模拟, 再根据功能梯度材料Euler-Bernoulli梁和Timoshenko梁的屈曲控制方程及其闭合解, 由传递矩阵法建立了求解含裂纹功能梯度材料梁在多种边界条件下屈曲载荷的循环递推公式和特征行列式, 使问题通过降阶的方法得到快速准确的解答。数值算例研究了剪切变形、 裂纹的不同数目及位置、 材料参数变化、 长细比和不同边界约束条件等对含裂纹功能梯度材料梁屈曲载荷的影响。结果表明该方法可以简单、 方便和准确地计算不同数目裂纹和任意边界条件下功能梯度材料梁的屈曲问题。      

Structural damage identification using transfer matrix with lumped crack properties

A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measured and predicted displacements. The method is verified using several numerical models as well as experiments with cracked beams. The TM is shown to be suitable for local identification and also fast and accurate compare to other methods.     

基于遗传神经网络与模态应变能的斜裂缝两阶段诊断方法

基于遗传神经网络与模态应变能,提出了一种斜裂缝两阶段诊断方法,识别梁体中斜裂缝的位置、角度和深度。根据线弹性断裂力学与虚功原理,推导了斜裂缝梁的单元刚度矩阵,得到了其频率与振型。采用遗传算法对BP神经网络的拓扑结构、权值和阈值进行优化,从而建立了遗传神经网络,用于识别梁体中斜裂缝的位置和角度;结合斜裂缝单元的模态应变能,通过对斜裂缝应力强度因子的积分,得到斜裂缝深度的解析表达式,用于识别斜裂缝的深度。数值仿真表明:能够高精度地诊断出梁体中斜裂缝的损伤状态,包括位置、角度和深度;与BP神经网络相比,遗传神经网络具有更强的泛化能力,且对测量噪声具有较好的鲁棒性。     

Detection of multiple cracks using frequency measurements

A method for detection of multiple open cracks in a slender Euler-Bernoulli beams is presented based on frequency measurements. The method is based on the approach given by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841], transverse vibration modelling through transfer matrix method and representation of a crack by rotational spring. The beam is virtually divided into a number of segments, which can be decided by the analyst, and each of them is considered to be associated with a damage parameter. The procedure gives a linear relationship explicitly between the changes in natural frequencies of the beam and the damage parameters. These parameters are determined from the knowledge of changes in the natural frequencies. After obtaining them, each is treated in turn to exactly pinpoint the crack location in the segment and determine its size. The forward, or natural frequency determination, problems are examined in the passing. The method is approximate, but it can handle segmented beams, any boundary conditions, intermediate spring or rigid supports, etc. It eliminates the need for any symbolic computation which is envisaged by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841] to obtain mode shapes of the corresponding uncracked beams. The proposed method gives a clear insight into the whole analysis. Case studies (numerical) are presented to demonstrate the method effectiveness for two simultaneous cracks of size 10% and more of section depth. The differences between the actual and predicted crack locations and sizes are less than 10% and 15% respectively. The numbers of segments into which the beam is virtually divided limits the maximum number of cracks that can be handled. The difference in the forward problem is less than 5%.     

Online detection of the breathing crack using an adaptive tracking technique

Summary Early detection of structural damage is an important goal of any structural health monitoring system. Among numerous data analysis techniques, those which are used for online damage detection have received considerable attention recently, although the problem of online detection in continuous structures, for example beams, is quite challenging. In this paper, it is shown how the type, the size and the location of breathing cracks are identified online with the use of the records which are gathered from a continuous beam. For determining the existence of a breathing crack in a beam, its vibrating behavior is simulated. The algorithm of the least square estimation with the use of adaptive tracking is employed for identification purposes. This algorithm is capable of detecting the abrupt changes in problem parameters and traces its variations. With the use of reducing domain algorithm, this identification method shows better results and can detect the breathing crack in beams more efficiently. Finally, it is shown that with the use of sufficient mode shapes the method is capable of identifying the breathing crack in beams and frames. The efficiency of the proposed algorithm is shown through some case studies.     

薄壁曲梁的横向弯曲稳定分析

根据势能驻值原理,从曲梁的变形几何方程出发,采用转换B3样条函数模拟薄壁杆件横截面的纵向位移场,得到含非线性应变的薄壁曲梁的能量方程,采用样条有限杆元法求解薄壁曲梁的横向弯曲稳定问题。方法很好地描述了薄壁曲梁的翘曲位移和剪滞效应,为分析薄壁曲梁弯扭问题提供了一种有效的方法。数值算例表明本方法的前处理简单、收敛速度快,精度高。     

线弹性土壤中埋设悬跨管道的屈曲分析

建立了两端埋设在线弹性土壤中的悬跨管道的屈曲方程。利用细长梁小挠度理论,建立了含有轴向压力的悬跨段和埋设段管道的弯曲控制方程。基于埋设段管道的刚度和变形特性,建立了符合悬跨段管道实际情况的边界条件。导出了悬跨段管道对称屈曲和反对称屈曲的屈曲载荷方程,通过数值求解给出了不同土壤刚度系数条件下悬跨段管道屈曲载荷。研究表明:悬跨段管道的屈曲载荷系数依赖于土壤刚度系数,简支梁模型只在特定的土壤刚度系数下适用于悬跨管道;在土壤刚度系数很大时,两端固支梁模型才能反映悬跨管道的屈曲特性。建议采用该方法进行埋设悬跨管道的屈曲分析。     

湿-热-机-弹耦合FGM梁的稳定性及振动特性

研究了初始轴向机械载荷作用下Winkler-Pasternak弹性地基上功能梯度材料（FGM）梁在湿-热环境中的稳定性及振动特性。假设温度和湿度沿梁厚度方向稳态分布,材料的物性依赖于温度且按Voigt混合幂律模型连续分布。首先,基于一种扩展的n阶广义梁理论,应用Hamilton原理,统一建立了以轴向位移、弯曲变形项挠度及剪切变形项挠度为基本未知函数FGM梁的屈曲及自由振动方程,采用Navier解法获得了FGM简支梁静动态响应的精确解。其次,通过算例验证并给出了该广义梁理论阶次n的理想取值,丰富梁理论的同时,可供验证或改进其他各种剪切变形梁理论。最后,着重探讨了3种湿-热分布下湿度与温度增加、初始轴向机械载荷、跨厚比、地基刚度、梯度指标等诸多参数对FGM梁稳定性和振动特性的影响。