An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Key stress extraction and equivalent test method for hybrid DC circuit breaker

Firstly, relevant stress properties of millisecond level breaking process and microsecond level commutation process of hybrid HVDC circuit breaker are studied in detail on the basis of the analysis for the application environment and topological structure and operating principles of hybrid circuit breakers, and key stress parameters in transient state process of two time dimensions are extracted. The established digital simulation circuit for PSCAD/EMTDC device-level operation of the circuit breaker has verified the stress properties of millisecond level breaking process and microsecond level commutation process. Then, equivalent test method, circuits and parameters based on LC power supply are proposed on the basis of stress extraction. Finally, the results of implemented breaking tests for complete 200 kV circuit breaker, 100 kV and 50 kV circuit breaker units, as well as single power electronic module have verified the accuracy of the simulation circuit and mathematical analysis. The result of this paper can be a guide to electrical structure and test system design of hybrid HVDC circuit breaker.

Analysis and Research on Mechanical Stress and Multiobjective Optimization of Synchronous Reluctance Motor

The mechanical strength of the synchronous reluctance motor(SynRM)has always been a great challenge.This paper presents an analysis method for assessing stress equivalence and magnetic bridge stress interaction,along with a multiobjective optimization approach.Considering the complex flux barrier structure and inevitable stress concentration at the bridge,the finite element model suitable for SynRM is established.Initially,a neural network structure with two inputs,one output,and three layers is established.Continuous functions are constructed to enhance accuracy.Additionally,the equivalent stress can be converted into a contour distribution of a three-dimensional stress graph.The contour line distribution illustrates the matching scheme for magnetic bridge lengths under equivalent stress.Moreover,the paper explores the analysis of magnetic bridge interaction stress.The optimization levels corresponding to the length of each magnetic bridge are defined,and each level is analyzed by the finite element method.The Taguchi method is used to determine the specific gravity of the stress source on each magnetic bridge.Based on this,a multiobjective optimization employing the Multiobjective Particle Swarm Optimization(MOPSO)technique is introduced.By taking the rotor magnetic bridge as the design parameter,ten optimization objectives including air-gap flux density,sinusoidal property,average torque,torque ripple,and mechanical stress are optimized.The relationship between the optimization objectives and the design parameters can be obtained based on the response surface method(RSM)to avoid too many experimental samples.The optimized model is compared with the initial model,and the optimized effect is verified.Finally,the temperature distribution of under rated working conditions is analyzed,providing support for addressing thermal stress as mentioned earlier.

The Stress Combination Method for the Fatigue Assessment of the Hatch Corner of a Bulk Carrier Based on Equivalent Waves

The stress combination method for the fatigue assessment of the hatch comer of a bulk carrier was investigated based on equivalent waves. The principles of the equivalent waves of ship structures were given, including the determination of the dominant load parameter, heading, frequency, and amplitude of the equivalent regular waves. The dominant load parameters of the hatch comer of a bulk carrier were identified by the structural stress response analysis, and then a series of equivalent regular waves were defined based on these parameters. A combination method of the structural stress ranges under the different equivalent waves was developed for the fatigue analysis. The combination factors were obtained by least square regression analysis with the stress ranges derived from spectral fatigue analysis as the target value. The proposed method was applied to the hatch comer of another bulk carrier as an example. This shows that the results from the equivalent wave approach agree well with those from the spectral fatigue analysis. The workload is reduced substantially. This method can be referenced in the fatigue assessment of the hatch comer of a bulk carrier.

Finite Element Analysis of In-Plane Displacements and Von-Mises Stresses in Ellipsoidal and Circular Cylinderical Petroleum Tankers

Road tankers are the most used means of transporting petroleum product to end users due to its cost effectiveness and energy-efficiency. The cylindrical tank has been well designed for by ASME VIII divisions 1 and 2 using analytical equations. Petrol tankers are not circular but elliptical probably for stability during transportation. This paper has used the finite element method to investigate in-plane displacements and Von-Mises stresses in both circular and elliptical cylindrical tanks under full loading. An elliptical OANDO? tanker of 66.78 m3volume and shell thickness of0.2 mmand an equivalent volume circular cylindrical tank was used for the simulation. MATLAB? was used to generate geometrical mesh model of the petroleum tankers, extract element coordinates and conduct the finite element analysis. Plane strain condition was used in analyzing a section of the petroleum tanker. It was observed that an equivalent volume circular cylindrical tank was under a higher internal pressure (16,858 N/m2) compared to the elliptical cylinder (14,480 N/m2). Von-Mises stress and in-plane displacements showed direct linear relationships with internal fluid pressure. Von-Mises stress in the elliptical tank was found to be lower (5.7 × 106 N/m2) than for the circular tank (8 × 106 N/m2). In plane displacements was zero in the longitudinal direction for both tanks and of the order of 10-4 mm in the y-direction for both tanks with the circular larger by about 2.5 × 10-3 cm. So in addition to tank stability on the lorry, the Von-Mises stresses were lower as well for the elliptical tank. It was also observed that Von-Mises stresses were far below the yield stress of the steel plate. However, the effect of weldment area on lowering of yield stress was not studied. Stress values were validated using analytical method and found to be insignificantly different (P > 0.05).

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Equivalent circuit with complex physical constants and equivalent-parameters-expressed dissipation factors of piezoelectric materials

The equivalent circuit with complex physical constants for a piezoelectric ceramic in thickness mode is established. In the equivalent circuit, electric components （equivalent circuit parameters） are connected to real and imaginary parts of complex physical coefficients of piezoelectric materials. Based on definitions of dissipation factors, three of them （dielectric, elastic and piezoelectric dissipation factors） are represented by equivalent circuit parameters. Since the equivalent circuit parameters are detectable, the dissipation factors can be easily obtained. In the experiments, the temperature and the stress responses of the three dissipation factors are measured.

TIME-TEMPERATURE-STRESS EQUIVALENCE AND ITS APPLICATION TO NONLINEAR VISCOELASTIC MATERIALS

Stress-dependence of the intrinsic time of viscoelastic materialsis investigated. The influence of stress level on the intrinsic timeis considered to be similar to that of temperature, pressure, solventcon- centration, damage and physical aging. Thetime-temperature-stress equivalence principle is proposed, byemploying which, the creep curves at different temperatures andstress level can be shifted into a master curve at referencetemperature and stress level.

RPC应力-应变曲线系数与塑性损伤因子无量纲化计算模型研究

为了方便活性粉末混凝土(Reactive Powder Concrete,RPC)等效矩形应力图系数与塑性损伤因子的计算与取值,对RPC应力-应变曲线系数与塑性损伤因子的计算模型进行了理论研究。通过对现有的计算方法进行无量纲化转化,推导了决定计算模型的四个原函数条件;对一个实际的应力-应变关系进行了计算,将得到的结果进行了分析;并对受弯矩形梁非极限状态下截面内力和力矩的推定计算进行了演示。针对应力-应变关系式含有非整次有理分式的情况提出了曲线拟合方法;研究了拟合次数、拟合区间和拟合函数类型对拟合精度与稳定性的影响。比较了4种典型的RPC本构模型在同种材料下的应力-应变曲线系数与损伤因子取值模型曲线,结果显示:拟合曲线得到的取值模型与其他原始曲线得到的取值模型在曲线上具有较高的相似度,证明了曲线拟合方法的准确可靠性;最后给出了一种RPC受压应力-应变曲线系数与塑性损伤因子无量纲化取值模型。

基于温度--应力试验的混凝土温度应力仿真

为分析早龄期混凝土的温度变形和温度应力,使用ABAQUS有限元分析软件,考虑混凝土的热膨胀系数和弹性模量随等效龄期的变化规律,通过现有的堆石坝面板混凝土温度—应力试验测试数据建立温度—应力试验试件有限元分析模型,开展混凝土温度变形对应的温度场和应力场的数值仿真研究。研究结果表明:使用等效龄期,考虑早龄期混凝土热膨胀系数、弹性模量的时变性,可以提高温度应力场仿真模拟的精度,为实际工程提供更安全的设计依据。

基于应力等效关系的汽车零部件疲劳寿命预测模型

对于预测多级应力加载下的汽车零部件疲劳寿命,已有的相关非线性模型通常需要依赖大量的试验数据,或者较难选取合适的基准值,使得疲劳可靠性理论在汽车领域的应用存在一定局限性。针对此问题,基于材料疲劳寿命特性曲线,通过分析两级应力之间疲劳损伤转化过程,建立了一种考虑相邻载荷作用的等效转化关系,推导了两级、三级及更高应力等级情况下相邻应力之间的疲劳累积损伤等效公式和剩余疲劳寿命的表达式,进而提出了一种基于应力等效关系的疲劳寿命预测模型。该模型的计算过程仅需不低于两级应力的材料疲劳寿命试验结果。采用二级、三级、四级及五级应力加载试验数据,分别计算并对比了Miner模型、Manson模型、Subramanyan模型、Hashin模型及新模型的相对误差平均值和最大值,进一步汇总了两级至五级应力下各模型疲劳累积损伤与疲劳累积寿命的预测结果、各模型预测疲劳损伤与试验疲劳损伤之差的分布。结果表明,基于相邻载荷作用等效转化的新模型在疲劳寿命的整体预测结果优于Miner模型、Manson模型、Subramanyan模型及Hashin模型,可更为准确地应用于材料多级应力下的疲劳寿命/损伤预测。

有效减小大细长比微结构电铸层残余应力的兆声辅助微电铸方法

在利用微电铸工艺制作微机电系统(MEMS)开关的过程中,针对离心保险锁结构因电铸层残余应力大而出现翘曲、扭转等变形问题,采用兆声辅助微电铸方法减小电铸层残余应力。为探究兆声波对电铸层残余应力的影响,基于等效参考温度(ERT)法,建立兆声作用下离心保险锁微结构电铸层残余应力的仿真模型以优选兆声辅助微电铸的工艺参数——兆声功率密度。仿真结果表明,随着兆声功率密度的增大,离心保险锁的残余应力呈现先减小后增大的趋势,当兆声功率密度为2.54 W/cm^(2)时,离心保险锁的最大残余应力为52.58 MPa,相较于无兆声作用时减小了85.4%。在数值模拟的基础上进行微电铸实验验证研究。实验结果表明:兆声功率密度为2.54 W/cm^(2)时,大细长比微结构的变形量减小了88.6%,实验结果与仿真结果一致。在上述仿真结果和实验研究的基础上,制作出了高800μm、细长比高达1∶70的离心保险锁结构,并完成MEMS开关的制作与装配。

超大跨劲性骨架拱桥缩尺模型试验方案设计研究

为对超大跨劲性骨架拱桥缩尺模型试验方案进行合理设计,以计算跨径600 m的劲性骨架拱桥——天峨龙滩特大桥为背景,围绕模型缩尺比、结构设计、材料及加载系统等关键环节,开展主拱圈缩尺模型试验方案设计研究。最终确定模型拱缩尺比为1∶10,劲性钢骨架采用单肋形式,采用与实桥主拱圈性能相近、便于施工的材料,采用阵列式滑轮组加载系统实现模型拱和实桥主拱圈的应力等效,还原外包混凝土分环分段浇筑施工,并简化劲性钢骨架与管内混凝土施工。将模型拱外包混凝土应力实测值、ANSYS建模计算得到的模型拱理论值及实桥主拱圈理论值进行对比,结果表明:模型拱和实桥主拱圈外包混凝土在施工阶段的应力变化趋势基本相同,最大绝对误差在2 MPa以内,模型拱应力实测值和理论值也吻合较好,缩尺模型试验方案设计合理。

基于正交试验的蓄能弹簧优化设计

为了提高蓄能弹簧的回弹性能,采用Ansys Workbench有限元软件建立了蓄能弹簧的有限元模型,并通过对比试验验证了模型的可靠性。以弹性能和最大等效应力作为回弹性能的评价指标,探究了薄片宽度、薄片厚度、截面直径、盘绕圈数以及盘绕中径等参数对蓄能弹簧回弹性能的影响。通过正交试验分析了各结构参数对蓄能弹簧的弹性能和等效应力的敏感性。基于弹性能最大和等效应力最小两个目标,对蓄能弹簧的结构参数进行了优化设计。研究结果表明:蓄能弹簧的弹性能随着薄片宽度、薄片厚度、截面直径以及盘绕圈数的增大而增大;最大等效应力随着薄片宽度增大而增大,随着截面直径和盘绕圈数的增大而减小;薄片厚度对弹性能的影响最大,盘绕圈数对最大等效应力的影响最大,而盘绕中径对弹性能与最大等效应力的影响均最小;优化后的蓄能弹簧弹性能提升了190.14%,同时等效应力峰值下降了2.26%。

高度修正实现刚度等效的梁结构有限元建模方法

民用飞机中对于梁结构的有限元建模,一般采用刚度等效方法将梁建成杆单元与剪切板单元的组合形式,这种有限元简化方法仅能保证截面刚度与真实截面刚度近似等效,但有限元中的截面面积与实际面积却相差较大,致使有限元分析的结果不能准确反映结构严重部位的应力情况。针对传统刚度等效有限元建模方法的不足,提出一种采用高度修正的刚度等效有限元建模方法;将该方法的计算结果与传统建模方法的计算结果、理论计算结果、试验测量结果进行对比。结果表明:本文提出的高度修正的有限元建模方法比传统杆板系建模方法更准确,与试验结果更接近;将该方法用于民用飞机结构有限元建模,能够对真实结构进行更准确地模拟,分析结果也更精确。

含点蚀缺陷高钢级弯管的极限承载能力研究

在油气管道运输过程中,由于荷载和腐蚀介质等因素,弯管相比直管更容易发生腐蚀。以点蚀缺陷为研究对象,建立含有点蚀缺陷弯管的三维非线性有限元模型,进一步分析了点蚀缺陷的位置、缺陷的几何形状和管材性能等因素对弯管极限内压的影响。研究结果表明,含点蚀缺陷弯管的极限内压受缺陷相对位置的影响,当缺陷位于弯管的内拱时,弯管的极限内压最小;含点蚀缺陷弯管的极限内压同样受缺陷尺寸的影响,极限内压随点蚀缺陷深度增加而减小,随点蚀缺陷半径增大而减小;管道尺寸、管道弯曲半径和管材性能等敏感因素也会对管道极限内压产生影响。研究结论对于含缺陷弯管的安全评定有一定的参考价值。

钢桥面板对接焊缝表面多缺陷疲劳效应研究

为探明钢桥面板对接焊缝焊趾区域共面及异面表面多缺陷在裂纹扩展过程中的形态变化及相互作用机制,以钢桥面板U肋下翼缘对接焊缝简化后的基本焊接构造为研究对象,探明对接焊缝焊接区域的应力强度因子KI分布,并在验证ABAQUS与FRANC3D数值模拟方法可靠性的基础上,对焊趾区域植入的共面或异面多裂纹进行多裂纹扩展分析。研究结果表明:含余高对接焊缝在轴拉荷载作用下,焊趾线附近存在应力强度因子KI的峰值点;相邻共面裂纹在扩展至临界深度的过程中存在裂纹融合前、裂纹融合时及裂纹融合后3个典型的扩展阶段,不同阶段裂纹前沿形态及扩展速率da/dN变化可通过等效应力强度因子幅值ΔK_(eff)的分布来体现;共面裂纹融合前,单裂纹靠近另一裂纹长轴端点的裂纹相互作用比例因子随净间距s1与裂纹深度a比值呈幂次负相关性;对接焊缝异面裂纹中焊趾处裂纹对热影响区裂纹存在抑制作用,并随着裂纹尺寸差异的累计增加,焊趾处裂纹对热影响区的抑制作用呈线性扩大,最终使得热影响区裂纹ΔK_(eff)低于门槛值ΔKth而失去活性停止扩展,上述抑制作用随异面净间距s2的增加而减弱。

航空发动机液压弯管流固耦合振动特性分析

为研究流固耦合作用下多弯曲段液压管道的流体流动与管道振动之间的动力学特性,基于ANSYS Workbench平台分析了航空发动机某易故障部位弯形液压管道的预应力模态,通过SST k-ω湍流模型模拟计算不同流体流速下弯形液压管内流体的流动状态,获得了不同管内流体流速与管道形变以及等效应力之间的关系,得出在允许最大流速下弯管的形变随曲率半径的变化趋势,并总结出该液压弯管不同充液状态下的前六阶固有频率的变化趋势。结果表明:管道形变随流体流速的增加而增大,随曲率半径的增大而减小;弯管不同充液状态下管道的前六阶固有频率随阶数增加而增长且同阶下空管的固有频率大于充液弯管的固有频率;最后通过充液弯管的前六阶振型图分析了不同阶频率易发生形变的部位研究,可为航空发动机弯形液压管道的设计提供参考。

正交异性钢桥面板双轴疲劳性能评估

为精确评估正交异性钢桥面板在双轴应力状态下的疲劳性能,以东营胜利黄河大桥为背景,建立该桥正交异性钢桥面板顶板、U肋、横隔板交叉连接部位焊缝的节段三维有限元模型,采用等效结构应力法对正交异性钢桥面板体系的双轴疲劳问题进行研究;通过模型试验验证正交异性钢桥面板体系的双轴疲劳特性,并进行其构造细节疲劳寿命评估。结果表明:弧形切口起焊点的疲劳裂纹萌生位置在横隔板下方焊趾处,经历裂纹萌生、裂纹稳定扩展和裂纹失效3个阶段,最终失效阶段裂纹形式为Ⅱ型裂纹主导的Ⅰ-Ⅱ型复合裂纹,此为该桥正交异性钢桥面板结构体系的主导疲劳失效模式;顶板焊缝焊趾及弧形切口起焊点焊趾处于双轴应力状态,面内剪切结构应力幅对疲劳应力的影响显著,按单轴疲劳应力进行寿命预测误差较大,按单轴疲劳应力状态对结构进行疲劳寿命设计偏于不安全;基于组合等效结构应力法的计算值与试验值吻合较好,各焊接细节计算得到的最大值下的疲劳裂纹起裂位置均与试验结果一致,按双轴疲劳应力预测疲劳寿命与试验值吻合较好,疲劳寿命评价精确度较高。

基于SPH法的磨料射流破损混凝土裂纹扩展及损伤分析

为研究射流冲击下混凝土的破损机理与裂纹扩展规律,基于光滑粒子流体动力学(smooth particle hydrodynamics,SPH)方法建立了磨料水射流冲击混凝土的数值模型,研究了混凝土内部的应力传播和破损方式,磨料体积分数和混凝土的孔隙率与裂纹长度、失效粒子数、坑深和坑径之间的关系。研究表明:裂纹对应力具有强阻碍作用,与边界应力波的反射叠加会使得应力区域性集中,形成中心微裂纹,以及内部破碎块;磨料体积分数为20%与0%相比,裂纹长度增加2.30倍,失效粒子数增加3.38倍,坑深值增加4.00倍,证明射流中添加磨料会大幅提高破损效果;混凝土的孔隙率越大,裂纹分布越发散,损伤区域面积、损伤程度和分形维数越大,证明孔隙会降低混凝土的抗压强度,孔隙率大的材料更易受损。