An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.

FLEXURAL WAVE PROPAGATION IN NARROW MINDLIN'S PLATE

Appling Mindlin＇s theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories, the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.

Fatigue Crack Propagation Analysis of Orthotropic Steel Bridge with Crack Tip Elastoplastic Consideration

Due to the complex structure and dense weld of the orthotropic steel bridge deck(OSBD),fatigue cracks are prone to occur in the typical welding details.Welding residual stress(WRS)will cause a plastic zone at the crack tip.In this paper,an elastoplastic constitutive model based on the Chaboche kinematic hardening model was introduced,and the extended finite element method(XFEM)was used to study the influence of material elastoplasticity and crack tip plastic zone on the law of fatigue crack propagation.By judging the stress state of the residual stress field at the crack tip and selecting different crack propagation rate models to investigate the crack propagation law when plastic deformation was considered,the propagation path and propagation rate of fatigue crack of the OSBD were obtained.The results show that,whether the residual stress field is considered or not,the plastic deformation at the crack tip will not cause the obvious closure of the fatigue crack at the U-rib toe during the crack propagation process,but will significantly affect the crack propagation path.When material plasticity is considered,the propagation angle of fatigue crack at the U-rib toe basically remains unchanged along the short-axis direction of the initial crack,but is going up along the long-axis direction,and the crack tip plastic zone inhibits the propagation of the crack tip on one side.Compared with linear elastic materials,the crack propagation law considering material plasticity is more consistent with that in actual bridge engineering.In terms of the propagation rate,if the residual stress field is not considered,the fatigue crack propagation rate at U-rib toe with plasticity considered is slightly higher than that without plasticity considered,because plastic deformation will affect the amplitude of energy release rate.When considering the WRS field,the fatigue crack propagation rate at U-rib toe is increased due to the combined actions of plastic deformation and stress ratio R.

Stable Fatigue Crack Propagation of 16MnR Steel

A research on the stable fatigue crack propagation of 16MnR steel is investigated systematically in this paper.First,control experiments of 16MnR with compact tension specimen is conducted to study the effect of R-ratios,specimen thickness and notch sizes.The experiments show that the fatigue crack growth(FCG)rate in stable propagation was insensitive to these factors.Then,the stress intensity factor(SIF)is computed and compared by displacement interpolation method,J integral and interaction integral method respectively.The simulation shows that optimization on the mesh density and the angle of singular element improved the computational efficiency and accuracy of SIF and the interaction integral method has an obvious advantage on stability.Finally,the FCG rate is modeled by the Jiang fatigue damage criterion and the extended finite element method(XFEM)respectively.The simulation results of FCG rate are in line with experiments data and indicate that XFEM method is more accurate than Jiang fatigue damage method.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.

Exact Traveling Wave Solutions for Nano-Solitons of Ionic Waves Propagation along Microtubules in Living Cells and Nano-Ionic Currents of MTs

In this work, the extended Jacobian elliptic function expansion method is used as the first time to evaluate the exact traveling wave solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to nano-solitons of ionic waves propagation along microtubules in living cells and nano-ionic currents of MTs which play an important role in biology.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

Uncertainty propagation analysis by an extended sparse grid technique

In this paper,an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle,aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function(PDF)of the system response.The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis.Moreover,assisted by the Rosenblatt transformation,the various types of extended integration points are transformed into the extended Gauss-Hermite integration points,which makes the method suitable for any type of continuous distribution.Subsequently,within the sparse grid numerical integration framework,the statistical moments of the system response are obtained based on the transformed points.Furthermore,based on the maximum entropy principle,the obtained first four-order statistical moments are used to fit the PDF of the system response.Finally,three numerical examples are investigated to demonstrate the effectiveness of the proposed method,which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

Loopy belief propagation based data association for extended target tracking

The data association problem of multiple extended target tracking is very challenging because each target may generate multiple measurements.Recently,the belief propagation based multiple target tracking algorithms with high efficiency have been a research focus.Different from the belief propagation based Extended Target tracking based on Belief Propagation(ET-BP)algorithm proposed in our previous work,a new graphical model formulation of data association for multiple extended target tracking is proposed in this paper.The proposed formulation can be solved by the Loopy Belief Propagation(LBP)algorithm.Furthermore,the simplified measurement set in the ET-BP algorithm is modified to improve tracking accuracy.Finally,experiment results show that the proposed algorithm has better performance than the ET-BP and joint probabilistic data association based on the simplified measurement set algorithms in terms of accuracy and efficiency.Additionally,the convergence of the proposed algorithm is verified in the simulations.

考虑坝-基-库水相互作用的拱坝底缝开裂模拟

针对拱坝裂纹扩展问题,以某拱坝为例,建立了大坝-地基-库水系统的三维有限元模型.在此基础上,基于全耦合的拱坝-地基-库水模型,利用扩展有限元法(extended finite element methods,XFEM)对地震作用下的底缝开裂进行了模拟分析.研究中,在坝体上游底部设置了不同位置的人工短缝,以探讨拱坝在强震条件下的底缝开裂响应.结果表明:横缝削弱了坝体的整体性,增大了坝体的位移响应,但增设横缝可有效减小坝体的应力响应;在坝体底部设置人工短缝显著降低了坝踵的应力响应;拱坝的横缝对底缝开裂影响显著,能限制底缝的横向扩展,减少坝体的开裂损伤.

径向井辅助前置液酸压裂缝扩展数值模拟

基于扩展有限元及双尺度连续模型理论建立径向井辅助前置液酸压裂缝扩展模型,引入偏离系数作为量化评价指标,分析各因素对裂缝形态的影响,并利用灰色关联分析方法明确主控因素。结果表明:径向井对前置液酸压裂缝扩展具有显著引导作用,裂缝优先沿径向井方向起裂并扩展一定距离,而后逐渐偏向最大水平主应力方向;径向井方位角、水平地应力差和地层弹性模量越小,径向井长度越长,偏离系数越小,径向井引导效果越好,其中水平地应力差为主控因素;当径向井方位角为15°时,前置液酸压裂缝沿着径向井方向扩展14.32 m后偏向最大水平主应力方向,径向井的引导效果最好,偏离系数为0.005。

水中高压电脉冲作用下径向预制裂纹扩展规律

为研究水中高压电脉冲作用下页岩多条预制裂纹同步扩展应力干扰作用对裂纹扩展影响,通过裂纹扩展轨迹、扩展长度、平均宽度、偏转角度和裂纹间等效应力分布的变化规律,综合考虑裂纹夹角、裂纹数量、水平地应力差等因素对裂纹起裂、扩展的影响。采用真三轴高压脉冲水力压裂试验平台进行实验室压裂试验和扩展有限元法(extended finite element method, XFEM)数值模拟计算,利用PCAS(pore and cracks analysis system)裂隙分析软件分析裂纹几何形态特征。结果表明:水中高压电脉冲作用下,预制裂纹可沿径向及轴向起裂、扩展;径向双裂纹间夹角越大,缝间干扰作用越弱,裂纹扩展曲折程度越好,扩展效果越好;等夹角径向三裂纹扩展,中间裂纹受应力干扰、受抑制作用最大,不等夹角径向三裂纹扩展,远离中间裂纹的右侧裂纹受干扰最小,扩展效果最好;随着水平地应力差增加,裂纹间应力干扰作用增强,裂纹扩展效果逐渐减弱。研究成果可为分析水中高压电脉冲作用下页岩多预制裂纹扩展过程和规律提供一定的参考。

随机轮载下钢桥面顶板与纵肋焊缝疲劳裂纹扩展特性研究

车辆轮迹横向分布是钢桥面板焊缝处产生随机应力谱的一项关键因素,加之焊接缺陷形态的随机性,诱发钢桥面板疲劳裂纹随机扩展行为。为了研究钢桥面顶板焊缝处疲劳裂纹的随机扩展特性,基于断裂力学理论与扩展有限元方法分析了轮迹横向分布对钢桥面板顶板焊根和焊趾等效应力强度因子的影响规律,揭示了轮迹横向分布离散度、初始裂纹深度和初始裂纹形态比对焊缝处疲劳裂纹随机扩展路径分布的影响规律。结果表明:轮载中心处于U肋正上方中心和焊缝中心位置分别为顶板焊趾和焊根的最不利横向加载工况;车辆轮迹横向分布对顶板焊根和顶板焊趾疲劳裂纹前缘应力强度因子影响差异显著,顶板焊根最大等效应力强度因子为85.99 MPa·mm^(1/2),比顶板焊趾增加了6.72%;轮迹横向分布离散度和初始裂纹深度与钢桥面板焊缝处疲劳裂纹随机扩展路径分布离散程度成正相关,初始裂纹形态比与其成负相关;焊缝细节初始裂纹深度越大,车辆荷载对其横向影响范围越大;焊缝细节初始裂纹形态比越大,车辆荷载对其横向影响范围变化不明显。

高速篦齿碰摩对封严环裂纹萌生与扩展影响研究

篦齿封严结构碰摩是航空发动机空气系统工作中存在的普遍问题,由于实际碰摩中难以观察到封严环上裂纹萌生与扩展的过程,采用有限元方法进行数值仿真能够对裂纹萌生与扩展过程和机理有更加深入的认识。建立碰摩后带磨损槽的封严环模型,考虑了封严环表面对流换热、碰摩力和碰摩温度,采用扩展有限元法(XFEM)对封严环碰摩温度场、应力场以及裂纹的萌生与扩展进行数值研究,并将仿真分析结果与碰摩试验裂纹结果进行对比。结果表明:数值仿真所得到的裂纹萌生位置及扩展方向均与碰摩试验中实际产生的裂纹基本一致,揭示了裂纹产生的机理,证明了该模型能够较好地模拟碰摩所导致的裂纹萌生与扩展过程。

非均质致密储层水平井分段压裂裂缝扩展模拟

针对非均质致密储层水平井分段压裂时裂缝的扩展延伸导致不同压裂缝簇产量差异大的问题,在考虑压裂液排量、黏度和地应力特征的情况下,开展非均质致密储层真三轴水力压裂实验和数值模拟研究,分析非均质岩石水平井分段压裂多裂缝扩展规律。结果表明:非均质性强的致密储层在水平井分段压裂时会产生不均一的裂缝形态,低两向水平应力差会强化储层非均质对裂缝形态差异性的影响,压裂液黏度对非均质储层改造时裂缝的形态影响相对较小,高弹性模量区域裂缝扩展相对更充分;数值模拟则证实储层非均质性会增加应力干扰的影响程度,通过改变弹性模量、压裂液排量等压裂参数均可以实现裂缝扩展的起裂扩展调控,因此对于非均质性较强的储层而言,有必要通过限流法或者暂堵等其他工艺手段进行水平井分段压裂施工,其中限流法可以保证不同位置的裂缝可以均衡进液,实现段内裂缝的同步和充分扩展,暂堵压裂则可以实现储层的充分打碎。研究成果有助于指导不同改造思路下的水平井压裂工艺优选。

致密油水平井多簇裂缝扩展数值模拟研究

大庆油田致密油水平井近年来主要采用密切割布缝进行压裂改造,多簇裂缝扩展将产生诱导应力,从而导致各簇裂缝延伸均匀程度不一致。为此,采用有限元软件ABAQUS建立了大庆油田致密油水平井多簇裂缝扩展数值模型,采用扩展有限元(XFEM)模拟方法,研究了2个布缝参数(簇距、段内簇数)、3个压裂施工参数(压裂工艺、施工排量及液体黏度)对裂缝扩展的影响。同时对比分析模拟结果与矿场实际光纤测试的各簇产能贡献结果,发现模拟的各簇裂缝长度与各簇的产油贡献具有很好的一致性,证实了模拟结果的正确性。模拟结果表明:当簇距缩小至5m时,各簇应力干扰明显,不利于裂缝扩展,当簇距达到10m及以上时,平均单簇裂缝半长变化不明显,合理簇距约为10m。平均单簇裂缝半长随段内簇数的增加呈增大趋势,但非均匀延伸程度也随之增大;与桥塞段内多簇同时改造相比,连续油管单簇依次改造模式更有利于裂缝延伸;平均单簇裂缝半长随施工排量的升高呈增大趋势,提高施工排量还能促进裂缝均匀延伸。平均单簇裂缝半长随液体黏度的升高呈增大趋势,可适当提高高黏液体比例。

焊接残余应力重分布与裂纹扩展的耦合分析

焊接残余应力对于焊接结构疲劳寿命影响明显,同时焊接残余应力并不是一成不变的,随着裂纹扩展会发生重分布。因此,开展焊接残余应力重分布和裂纹扩展的耦合研究对于准确预测焊接结构的疲劳寿命至关重要。本文基于热弹塑性有限元法与扩展有限元法(XFEM),提出考虑焊接残余应力重分布和裂纹扩展耦合的疲劳寿命分析方法。以TC4钛合金拉伸疲劳试样为例,结合扩展有限元法,研究焊接残余应力随裂纹扩展的重分布情况,循环迭代计算得到裂纹扩展过程中裂尖前方焊接残余应力分布,以及焊接残余应力重分布下的疲劳裂纹扩展a-N曲线。计算结果表明,裂尖处焊接残余应力会随裂纹扩展先增大后减小,相比于将焊接残余应力视为恒定值,考虑焊接残余应力重分布的扩展有限元疲劳寿命分析方法能更准确地预报焊接结构疲劳寿命。

初始裂纹倾角对圆柱滚子轴承次表面裂纹扩展的影响

为探究次表面裂纹倾斜角度对圆柱滚子轴承应力分布及裂纹扩展的影响,文章基于断裂力学、损伤力学等理论基础,应用扩展有限元法建立圆柱滚子轴承的有限元模型,模拟滚道次表面不同倾角的初始裂纹在外力载荷下的动态扩展过程,分析讨论次表面裂纹尖端的应力随裂纹倾角的变化情况以及裂纹尖端的应力对裂纹扩展的影响。模拟结果表明:在圆柱滚子压力载荷作用下,初始倾角在0°~30.0°范围内的次表面裂纹扩展主要受水平方向应力S 11的影响,次表面水平裂纹两端处的扩展同步对称进行;随着初始次表面裂纹逆时针旋转后倾角的增加,裂纹扩展速率增大,裂纹左端扩展长度增长,且增幅均由快到慢并趋于稳定状态,裂纹左端扩展角度增大,裂纹右端的扩展受到抑制。次表面裂纹的扩展速率、扩展长度、扩展角度比较结果表明,水平或较小角度的次表面裂纹扩展对损伤轴承寿命的影响较小。

基于XFEM的再生复合路面反射裂缝扩展研究

为了探究裂缝扩展路径及在不同条件下的扩展规律,该文基于ABAQUS软件中扩展有限元方法(extended finite element method,XFEM)模拟分析沥青混凝土半圆弯曲断裂试验中的裂缝扩展规律。通过对比他人试验及数值模型数据,验证了基于XFEM的有限元模型分析裂缝扩展的有效性。此外,该文建立干法油石分离再生复合路面二维模型,研究模型中施工缝宽度、预埋裂缝长度、偏转角及预设位置对裂缝尖端应力影响,结果表明尖端应力随着裂缝长度、偏转角增加而增大,而随着施工缝宽度增大呈现先减小后增大趋势,随着偏移距离变大则先增大后减小。该文研究结果有助于复合路面反射裂缝定量分析与表征,为复合路面设计及后期养护提供了参考与依据。

三维裂纹扩展的自适应虚拟节点法

在有限元方法的框架下针对三维裂纹扩展问题发展了自适应虚拟节点法。该方法采用无需裂尖加强函数(和相应的额外自由度)的虚拟节点技术描述裂纹处的间断,并采用单元局部水平集方法对三维裂纹面进行几何描述和追踪。为加速计算,提出了随裂纹面扩展的自适应网格加密方法。局部细化网格产生的悬空节点由简便的约束近似技术处理,无需引入额外自由度或特殊单元。发展的自适应虚拟节点法便于数值实现,具有与标准有限元方法相当的鲁棒性。数值结果表明,该方法可有效模拟三维裂纹扩展过程,且能方便地应用于复杂工程结构的多裂纹扩展问题。