Exact reconstruction of multiple concentrated damages on beams

In this paper, an exact procedure for the reconstruction of multiple concentrated damages on a straight beam is proposed. The concentrated damages are modelled as Dirac’s delta distributions capturing the effect of concentrated stiffness reduction. The presented procedure requires the knowledge of vibration mode shape displacements together with the relevant natural frequency, for the reconstruction of each damage position and intensity. The exact solution of the inverse problem at hand has been pursued by exploiting the analytical structure of the explicit closed form expressions provided for the vibration mode shapes of beams in the presence of an arbitrary number of cracks. The proposed procedure is first presented under the hypothesis that the displacements of a vibration mode shape are known at the cracked cross-sections. In this case, explicit closed form expressions of the crack severities are formulated. A further simple reconstruction approach allows the evaluation of the exact positions and intensity of the concentrated damages, if displacements of two vibration mode shapes are known at a single cross-section between two consecutive cracks. The proposed reconstruction procedure is applied for the identification of multiple cracks on a free–free beam where measurements have been simulated by means of a finite element analysis.     

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。     

含裂纹梁的动力响应

本文提出了一种计算含裂纹梁动力响应的有限元方法.采用时域方法辨识出模态参数,所得固有频率随裂纹长度和位置的变化值与实验结果吻合较好.计算了裂纹闭合而引起的结构响应变化,指出:外激励均值对固有频率影响较显著.最后,给出了判断裂纹位置的方法:用一阶振型和固有频率的差异确定;由不同测点频响函数变化来估计.     

含裂纹损伤杆系结构的动态特性研究

运用动刚度有限元法,研究了含裂纹损伤杆系结构的动态特性。提出了一种含裂纹的杆单元,基于断裂力学的线弹簧模型,导出了相应的动刚度矩阵。在此基础上,对含裂纹的悬臂梁和平面框架进行了数值计算,并与已有的实验值和解析解进行了比较。结果表明:损伤位置和损伤程度的不同均会导致结构动态特性发生改变,因而在结构分析中应考虑损伤的影响;而该单元能够方便地用于含裂纹损伤杆系结构的动态特性分析,并具有很好的精度。     

A two-dimensional elastic–plastic finite element analysis of friction effects on sliding crack surfaces in full or partial contact

Sliding crack surfaces are analysed, that are completely or partially in contact, using a two-dimensional plane-stress elastic–plastic finite element technique. Our in-house program was modified to account for the friction which acts between two rough mating surfaces. The analysis is applied to a cantilever beam cracked along its span through its centroidal plane. Twelve cracks with length-to-span ratios ranging from zero to 0.5 were analysed. The effect of friction was investigated by considering 0, 0.4, 0.8, 1.2 and 1.6 as values for the coefficient of friction with each crack length. The results show the influence of friction on the beam stiffness, strain energy release rate, modes of crack tip and surface displacements, and the development of plastic deformation. The present finite element outputs assist in the explanation of experimental events associated with mode II crack tip displacement data found in the literature.     

Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams

This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack propagation criterion, a simple remeshing procedure to accommodate crack propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load-deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.     

The continuous crack flexibility model for crack identification

The presence of a crack in a structural member introduces a local flexibility that affects its dynamic response. Moreover, the crack will open and close in time depending on the loading conditions and vibration amplitude. The changes in dynamic characteristics can be measured and lead to an identification of the structural changes which eventually might lead to the detection of a structural flaw. The results of various independent evaluations of changes in the natural frequency of vibrations of cracked structural elements are reported. A crack model of a continuous flexibility, found with fracture mechanics methods using the displacement field in the vicinity of the crack developed recently is used here. The analytical results for the cracked elements behaviour based on the continuous crack flexibility vibration theory were correlated with numerical solutions, the lumped-crack beam vibration analysis and experimental results obtained on aluminium and steel beams with open cracks.     

简支梁裂纹位置识别的一种简单方法

由等效线弹簧来模拟裂纹引起的软化效应,基于铁摩辛柯梁理论得到含裂纹简支梁横向振动的频率计算式,由此获得识别裂纹位置的一种近似方法。文中利用梁的二维有限元模态分析数据进行裂纹位置的识别,结果表明该法在较宽的高跨比范围内,有好的效果;裂纹的深度对识别精度影响不大。     

New crack‐tip elements for XFEM and applications to cohesive cracks

An extended finite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3‐node triangular elements and quadratic 6‐node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton–Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended finite element method are compared to reference solutions and show excellent agreement. Copyright © 2003 John Wiley & Sons, Ltd.     

基于小波有限元的悬臂梁裂纹识别

研究了悬臂梁裂纹识别中的正反问题．即通过裂纹位置和尺寸求解梁的固有频率以及利用梁的固有频率．识别裂纹位置和尺寸。以矩形截面裂纹悬臂梁为例，利用小波有限元方法建立了梁自由振动的有限元模型．其中裂纹被看作为一刚度已知的扭转线弹簧，求解出了系统的固有频率；通过行列式变换，将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题，分别做出了以不同固有频率作为输入值时裂纹位置与弹簧刚度之间的解曲线，曲线交点预测出裂纹的位置与尺寸。数值算例证实了算法的有效性，为工程结构裂纹故障预示与诊断提供了新的方法。     

Sub-Structural Parameter Identification Including Cracks of Beam Structure Using PZT Patch

This paper presents the numerical simulation of damage identification of beam structures using novel One Dimensional (1-D) PZT patch model with sub-structuring applied to the PZT Patch boundaries. The 1-D PZT patch model is simple and requires less computational effort than 2-D or 3-D models. A hybrid element constituted of 1-D beam element and a PZT sensor is used with reduced material properties which is very convenient for beams and is a novel application. The accuracy of 1-D hybrid element with cracked structure is first verified experimentally. The stiffness, damping and crack parameters are identified by minimizing the deviation between the predicted and measured voltage from the PZT patch using an optimization algorithm. The numerical signals are polluted with 5% Gaussian noise to simulate experimental noise. Numerical studies are performed on a beam and a nine member frame structure for sub-structural parameter and multiple crack identification. The PZT patches are attached at either ends of beam member to be identified. Sub-structuring is done to isolate the beam with patch, thus reducing the size of model to be identified. The numerical results show significant improvement in identification accuracy compared to other methods.     

基于谱元法的复合材料裂纹梁Lamb波传播特性研究

基于谱元法提出了一种弹簧元来模拟复合材料梁由于横向裂纹导致的轴弯耦合效应,分析复合材料裂纹梁中Lamb波的传播特性。由断裂力学的相关知识求得弹簧元的刚度,建立复合材料裂纹梁的损伤谱元模型。通过模拟复合材料裂纹梁内Lamb波传播,并和传统的有限元结果进行比较,验证了所提出模型的可行性和有效性。推导了频域内Lamb波各模态的能量计算公式,裂纹处的能量守恒证明了所提出模型的正确性,同时计算表明复合材料梁中裂纹处反射与透射的Lamb波各模态能量随着裂纹深度的变化规律具有单调性,结论可以为定量识别复合材料梁裂纹提供实用依据。     

Free vibration analysis of uniform and stepped cracked beams with circular cross sections

This paper presents a novel numerical technique applicable to analyse the free vibration analysis of uniform and stepped cracked beams with circular cross section. In this approach in which the finite element and component mode synthesis methods are used together, the beam is detached into parts from the crack section. These substructures are joined by using the flexibility matrices taking into account the interaction forces derived by virtue of fracture mechanics theory as the inverse of the compliance matrix found with the appropriate stress intensity factors and strain energy release rate expressions. To reveal the accuracy and effectiveness of the offered method, a number of numerical examples are given for free vibration analysis of beams with transverse non-propagating open cracks. Numerical results showing good agreement with the results of other available studies, address the effects of the location and depth of the cracks on the natural frequencies and mode shapes of the cracked beams. Modal characteristics of a cracked beam can be employed in the crack recognition process. The outcomes of the study verified that presented method is appropriate for the vibration analysis of uniform and stepped cracked beams with circular cross section.     

基于裂纹诱导弦挠度的Timoshenko梁裂纹无损检测

研究了基于Timoshenko梁静态挠度识别梁中裂纹位置及损伤程度的计算方法。首先,将梁开闭裂纹等效为单向旋转弹簧,利用Delta函数和Heaviside函数,得到了具有任意开闭裂纹数目梁的等效抗弯刚度,求得了开闭裂纹Timoshenko梁弯曲变形的显式闭合通解,给出了闭合通解待定常数的迭代求解方法。其次,建立了裂纹诱导弦挠度函数,证明了在裂纹处裂纹诱导弦挠度曲线斜率存在突变,为裂纹位置识别提供了理论依据。在此基础上,给出了裂纹等效旋转弹簧刚度的近似计算公式。最后,通过数值试验,将所建立的方法分别应用于裂纹位置及损伤程度已知的简支和固支Timosheoko梁裂纹位置识别和损伤程度计算,结果表明该文建立的裂纹损伤识别方法不仅具有一般的适用性,而且具有较高的精度和可靠性。     

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

This paper presents a detailed investigation on the modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam with hollow circular cross-section. To consider multiple crack effects, a cantilever beam including cracks is considered for six damage scenarios. Finite element models are constituted in ANSYS software for numerical solutions. The results are validated by experimental measurements. Ambient vibration tests are performed to extract the dynamic characteristics using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. Calculated and measured natural frequencies and mode shapes for undamaged and damaged beams are compared with each other. Automated model updating is carried out using the modal sensitivity method based on Bayesian parameter estimation to minimize the differences for damage detection. In addition, modal assurance criterion (MAC) and coordinated modal assurance criterion (COMAC) factors are obtained from the mode shapes and two set of measurements to establish the correlation between the measured and calculated values for damage location identification.     

Crack identification of beam structures using homotopy continuation algorithm

An approach based on homotopy continuation algorithm is presented to identify the parameters of a cracked beam. Euler–Bernoulli finite beam element with a fully opened crack model is adopted to establish the dynamic equation of the structural system. In the inverse problem, the homotopy equation is derived from minimizing the error between the calculated and the simulated measured acceleration responses. The range of homotopy parameter is divided into a number of divisions. Newton iterative method is employed to estimate the solution at each of these division points. The solution at the last division point corresponds to the homotopy equation matching the objective function. Numerical simulations with a simply supported beam and two-span beam show that the proposed method is very accurate compared to an existing method for both single and multiple cracks identification. The effects of type of excitation, division of the homotopy parameter and measurement noise on the identified results are discussed. It is noted that there is no need for an accurate set of initial values with the proposed approach.     

Strength of sandwich beams with mid-plane debondings in the core

Sandwich beams containing cracks in the mid-plane of the core are investigated. The cracked part is subjected to a constant remote shear stress field. Beams with different cross-section geometries and materials were analyzed by the finite element method (FEM) in order to compute the stress intensity factors at the crack tips. An analytical approach for estimation of the energy release rate, based on a potential energy calculation, is presented that agrees well with results from the FE analyses. Results from four-point bending tests with cracked beams show that the fracture load can be accurately predicted. The simplicity of the analytical model makes it possible to compute critical crack lengths and safety factors for various types of sandwich beams.     

Ritz analysis of discontinuous beams using local trigonometric functions

The objective of the current paper is to present a Ritz-type analytical model for predicting the behavior of discontinuous beams such as thin-walled beams with cracks and multiply-stepped beams. The beam is discretized in the cracked as well as the un-cracked domains for a cracked thin-walled beam and in uniform beams for a multiple-stepped beam. A set of local trigonometric trial functions is used to define the twist angle for the cracked domain and the un-cracked domains, as well as to define the displacement field for uniform domains. A global equation system of unknown Ritz coefficients is derived by minimizing the Lagrangian functional or the total potential energy. In the present Ritz model, the interface continuity conditions between sub-domains are investigated and enforced into the global equation system using the condensation procedure or the Lagrange multipliers. Examples are presented to illustrate the effectiveness of the current model for free vibration and torsional analysis. Results obtained from the current model are found to agree well with those obtained using a detailed finite element method or with existing results in literature. The proposed model offers an efficient approach to reduce the modeling efforts and computational time required to analyze complex beams with cracks or multiple steps.     

An investigation into the eigen-nature of cracked composite beams

It is known that the presence of cracks in composite structures introduces local flexibility associated with the changes in the dynamic characteristics of composite structures. However the nature and variations of the natural frequencies due to the presence of cracks, are still under discussion and analysis.

The present work introduces an attempt to study the variations in the eigen-nature of cracked composite beams due to different crack depths and locations. A numerical and experimental investigation has been made. The numerical finite element technique is utilized to compute the eigen pairs of laminated composite beams through several state of cracks. The model is based on elastic-plastic fracture mechanics techniques in order to consider the crack tip plasticity in the analysis. A finite element model has been developed to formulate the stiffness matrices for single edge cracked structural elements using transfer matrix theory. These matrices take into account the effects of axial, flexural and shear deformations due to crack presence. The present model has been applied to investigate the effects of state of crack, lamina code number, boundary condition on the dynamic behavior of composite beams.

The experimental tests and frequency response spectrums (FRS) is displayed on [FFT] analyzer. In experimental work the eigen pairs versus several state of cracks with various code number are measured using inductive hammering technique. The results show that the changes of the eigen parameters provide a proper indicator for detection and predication the current state of crack.     

含单侧预制裂纹梁的冲击动态断裂过程试验研究

利用动焦散线试验方法研究了冲击下预制裂纹梁的动态断裂行为,对比分析了冲击荷载作用下单裂纹与双裂纹试件的应力强度因子、扩展轨迹以及速度、加速度等参数的变化规律。试验结果表明:冲击荷载作用下,含双裂纹且主裂纹在冲击点正下方的试件起裂时间最早,裂纹扩展后期朝向次裂纹方向发生较小的偏移;含Ⅰ型单裂纹的试件起裂时间次之,裂纹扩展路径呈直线;含双裂纹且两条裂纹均偏置于冲击点的试件起裂时间最晚,扩展过程中发生明显的曲裂现象。同时,裂纹扩展过程中曲裂现象越严重,裂纹扩展的最大速度就越小。在落锤冲击试件到试件断裂的整个阶段,应力强度因子一直表现出振荡变化。含双裂纹的试件,在主裂纹扩展中期,次裂纹上的应力强度因子有一个快速下降的过程。