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.

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.

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.

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.

不同内固定系统治疗股骨转子间骨折的力学稳定性

背景:股骨转子间骨折的骨折类型和固定方式多样,各固定系统间的力学稳定性相差较大。使用有限元分析方法对各固定系统开展生物力学研究具有科学的临床意义。目的:通过有限元方法对比分析多种内固定应用于股骨A031-A2.1型转子间骨折的力学稳定性。方法:在已验证有效性的股骨有限元模型基础上,对模型进行必要的切割,造模成股骨A031-A2.1型转子间骨折,模拟临床手术方法置入不同的内固定系统,分别建立股骨近端防旋髓内钉、动力髋螺钉、经皮加压钢板和股骨近端锁定钢板固定模型。约束4组模型股骨远端下所有节点,在股骨头上施加700,1400和2100N的压缩载荷,通过计算分析,观察各组模型的等效应力分布和压缩刚度,比较各组模型之间的力学稳定性。结果与结论:①通过计算分析,对比各组模型的变形量计算压缩刚度后,在各级载荷作用下,各组模型上压缩刚度呈现的趋势:生理组>股骨近端防旋髓内钉组>股骨近端锁定钢板组>经皮加压钢板组>动力髋螺钉组;完整的生理组模型的压缩刚度明显高于所有的手术组模型;②观察应力指标,因存在应力遮挡效应,致使各固定组的应力峰值均高于生理组,最大峰值均集中分布于各内固定上;其中股骨近端防旋髓内钉固定组应力峰值最小,动力髋螺钉固定组应力最高,应力分布趋势呈现:生理组<股骨近端防旋髓内钉固定组<经皮加压钢板固定组<股骨近端锁定钢板固定组<动力髋螺钉固定组;③分布于骨质模型的应力,因内固定置入位置不同呈现不同的分布结果;④提示对于股骨转子间骨折,各种内固定均能起到有效的固定,结合有限元分析结果得出股骨近端防旋髓内钉组是较好的一种内固定选择,呈现变形量小、应力峰值低,应力分布均匀的特性;经皮加压钢板组和股骨近端锁定钢板组的力学效果优良,固定效果接近股骨近端防旋髓内钉固定;动力髋螺钉固定效果欠佳,同比于其他内固定,其力学稳定性较差。

不同弹性模量计算机辅助设计和计算机辅助制造桩核材料的应力分析

背景:桩核修复是牙体缺损修复的一种常规选择,然而不同桩核材料的修复效果存在差异。目的:利用有限元方法评估不同弹性模量桩核修复模型中桩核与牙根黏结剂部位的应力分布情况。方法:在三维建模软件中构建一个三维根管治疗过的上颌中切牙模型,进行全瓷冠修复,修复中的桩核材料分别使用纳米陶瓷树脂(弹性模量12.8 GPa)、复合树脂(弹性模量16 GPa)、混合陶瓷(弹性模量34.7 GPa)、玻璃陶瓷(弹性模量95 GPa)、钛合金(弹性模量112 GPa)和氧化锆(弹性模量209.3 GPa),将模型约束在皮质骨中,在中切牙牙冠舌侧1/3处加载与牙体长轴呈45°的100 N集中力,通过最大主应力分析修复模型中桩核、牙本质及桩与牙根黏结剂的应力分布。结果与结论:(1)当使用弹性模量较高的桩核材料时,修复模型中的桩核应力较集中;当使用弹性模量接近牙本质的桩核材料(纳米陶瓷树脂和复合树脂)时,桩核的应力分布较均匀;无论桩核材料如何,各修复模型中牙本质上的应力分布相似;使用弹性模量更高的桩核时,修复模型中桩与牙根黏结剂处显示出更多的应力集中。(2)纳米陶瓷树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为31.00,33.21,0.51 MPa,复合树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为36.84,33.14,0.59 MPa,混合陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为64.05,32.83,1.00 MPa,玻璃陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为112.30,32.69,1.73 MPa,钛合金模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为120.00,32.17,1.86 MPa,氧化锆模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为148.80,31.85,2.28 MPa。(3)桩核材料的弹性模量越高,进行桩核修复时桩核处的最大应力值越大,桩核材料弹性模量对修复模型中桩与牙根黏结剂处与牙本质的最大应力值无明显影响。

Methodology to Evaluate Fatigue Damage of High-Speed Train Welded Bogie Frames Based on On-Track Dynamic Stress Test Data

The current method of estimating the fatigue life of railway structures is to calculating the equivalent stress amplitude based on the measured stress data. However, the random of the measured data is not considered. In this paper, a new method was established to compute the equivalent stress amplitude to evaluate the fatigue damage based on the measurable randomness, since the equivalent stress is the key parameter for assessment of structure fatigue life and load derivation. The equivalent stress amplitude of a high-speed train welded bogie frame was found to obey normal distribution under uniform operation route that verified by on-track dynamic stress data, and the proposed model is, in effect, an improved version of the mathematical model used to calculate the equivalent stress amplitude. The data of a long-term, on-track dynamic stress test program was analyzed to find that the normal distribution parameters of equivalent stress amplitude values differ across different operation route. Thus, the fatigue damage of the high-speed train welded bogie frame can be evaluated by the proposed method if the running schedule of the train is known a priori. The results also showed that the equivalent stress amplitude of the region connected to the power system is more random than in other regions of the bogie frame.

Numerical analysis of loaded stress and central displacement of deep groove ball bearing

The aim of this work is to develop a three-dimensional model of deep groove ball bearing to investigate the loaded stresses and central displacements of bearing rings. The equivalent stresses and central displacements of bearing rings are obtained based on the simulated analysis. Moreover, several parameters, such as load magnitude, raceway groove curvature radius(RGCR), thicknesses of outer and inner rings, are varied to investigate their effects on the equivalent stresses and central displacements of bearing rings. Research results provide useful guidelines for determining the design parameters.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

A New Modified Conductivity Model for Prediction of Shear Yield Stress of Electrorheological Fluids Based on Face-center Square Structure

A new modified conductivity model was established to predict the shear yield stress of electrorheological fluids (ERF). By using a cell equivalent method, the present model can deal with the face-center square structure of ERF. Combining the scheme of the classical conductivity model for the single-chain structure, a new formula for the prediction of the shear yield stress of ERF was set up. The influences of the separation distance of the particles, the volume fraction of the particles and the applied electric field on the shear yield stress were investigated.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Advanced test methods of material property characterization:high strain-rate testing and experimental simulation of multiaxial stress states

Optimum utilization of the loading capability of engineering materials is an important and active contribution to protect nature's limited resources,and it is the key for economic design methods.In order to make use of the materials' resources,those must be known very well;but conventional test methods will offer only limited informational value.The range of questions raised is as wide as the application of engineering materials,and partially they are very specific.The development of huge computer powers enables numeric modelling to simulate structural behaviour in rather complex loading environments-so the real material behaviour is known under the given loading conditions.Here the art of material testing design starts.To study the material behaviour under very distinct and specific loading conditions makes it necessary to simulate different temperature ranges,loading speeds, environments etc.and mostly there doesn't exist any commonly agreed test standard.In this contribution two popular,non-standard test procedures and test systems will be discussed on the base of their application background,special design features as well as test results and typically gained information:The demand for highspeed tests up to 1000 s^(-1) of strain rate is very specific and originates primarily in the automotive industry and the answers enable CAE analysis of crashworthiness of vehicle structures under crash conditions.The information on the material behaviour under multiaxial loading conditions is a more general one.Multiaxial stress states can be reduced to an equivalent stress,which allows the evaluation of the material's constraint and criticality of stress state.Both discussed examples shall show that the open dialogue between the user and the producer of testing machines allows custom-tailored test solutions.

An Analysis of the Influence of Protective Films on the Inner Surfaces of CCPP Headers and Steam Pipelines on Their Thermal Stress State

At present, the main attention of researchers is paid to the deterioration of heat transfer when heating the outer surface of the pipe with the liquid or steam, flowing inside it, in the presence of films or deposits on its inner surface. However, when pipe is heating by heat carrier medium, flowing inside it, film on the inner pipe surface serve a dual protective function, protecting the pipe from corrosion and reducing its thermal stress. The article represents the results of the computational analysis of protective films influence on the thermal stressed state of headers and steam pipelines of combined-cycle power plants (CCPP) heat-recovery steam generators at different transient operating conditions particularly at startups from different initial temperature states and thermal shock. It is shown that protective films have a significant influence on the stresses magnitude and damage accumulation mainly for great temperature disturbances (for thermal shock). Calculations were carried out at various thicknesses of films and assuming that their thermal conductivity less than thermal conductivity of the steam pipelines metal.

2D and 3D Analysis of Magnetocardiographic Data in the Evaluation of the Ventricular Repolarization Changes under Exercise Stress Test in Patients with CAD

Objective: Non-invasive methods of evaluation of electrical activity of the heart are still the most important functional diagnostics methods in coronary artery disease (CAD) detection. It has been shown that magnetocardiography (MCG) appears to be rather sensitive in diagnostics of chronic CAD even in the patients at rest with unchanged ECG. The objective of present paper is to investigate the influence of non-invasive tests with a physical exerciseon MCG parameters in the patients with chronic CAD. Materials and Methods: In total, 10 patients were examined (mean age 41 ± 5 years) suffering from chronic stable angina (CAD). CAD was diagnosed by clinical evidences, bicycle ergometria positive data and coronary angiography (stenosis > 70% in at least onr main coronary angiography). The control group consisted of 14 healthy volunteers. MCG mapping was performed by means of a 7-channel SQUID-magnetometer installed in an unshielded room. The MCG examination was conducted twice, whilst patients were at rest and after exercise on the bicycle (in healthy persons it was conducted immediately after exercise and in the patients, after the ST depression and/or chest pain had disappeared). The homogeneity and electric motive force (EMF) direction disturbances on magnetic field distribution maps on an extent of ST-T interval have been evaluated. Results: Statistically significant differences between groups examined based both on 2D and 3D quantitative criteria were demonstrated. Conclusion: The application of a set of MCG criteria based on the analysis both of ventricular depolarization and repolarization will enable a greater degree of accuracy for the results of the exercise stress test, especially in doubtful cases.

Influence of Extended Bias Stress on the Electrical Parameters of Mixed Oxide Thin Film Transistors

This paper investigates the variation of electrical characteristic of indium gallium zinc oxide (IGZO) thin film transistors (TFTs) under gate bias stress. The devices are subjected to positive and negative gate bias stress for prolonged time periods. The effect of bias stress time and polarity on the transistor current equation is investigated and the underlying effects responsible for these variations are determined. Negative gate stress produces a positive shift in the threshold voltage. This can be noted as a variation from prior studies. Due to variation of power factor (n) from two, the integral method is implemented to extract threshold voltage (vt) and power factor (n). Effective, mobility (ueff), drain to source resistance (RDS) and constant k' is also extracted from the device characteristics. The unstressed value of n is deter-mined to be 2.5. The power factor increases with gate bias stress time. The distribution of states in the conduction band is revealed by the variation in power factor.

Effects of stress and physical ageing on nonlinear creep behavior of poly(methyl methacrylate)

The effects of stress,ageing time and ageing temperature on creep behavior of poly(methyl methacrylate) were studied.After annealing above its glass transition temperature for a period of time to eliminate the stress and thermal history,the specimens were quenched and aged at various ageing temperatures for different ageing time,and then the short-term creep tests under different stress levels were carried out at room temperature.The creep strains were modeled by means of time-ageing time equivalence and time-stress equivalence,and the master creep curves were constructed via ageing time shift factors and stress shift factors.The results indicate that the creep rate increases with stress,while decreases with ageing time,and the ageing temperature history obviously affects the creep rate.For linear viscoelastic material,the ageing shift rate is independent on imposed stress,while for nonlinear viscoelastic material,the ageing shift rate decreases with increasing stress.The unified master creep curve up to 540 d at reference state was constructed by shifting the creep curves horizontally along the logarithmic time axis to overlap each other.It is demonstrated that the time-stress equivalence,united with the time-ageing time equivalence,provides an effective accelerated characterization technique in the laboratory to evaluate the long-term creep behavior of physical ageing polymers.

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。