A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

A new slope optimization design based on limit curve method

A new method is proposed for slope optimization design based on the limit curve method, where the slope is in the limit equilibrium state when the limit slope curve determined by the slip-line field theory and the slope intersect at the toe of the slope. Compared with the strength reduction (SR) method, finite element limit analysis method, and the SR method based on Davis algorithm, the new method is suitable for determining the slope stability and limit slope angle (LSA). The optimal slope shape is determined based on a series of slope heights and LSA values, which increases the LSA by 2.45°-11.14° and reduces an invalid overburden amount of rocks by 9.15%, compared with the space mechanics theory. The proposed method gives the objective quantification index of instability criterion, and results in a significant engineering economy.

Prediction of forming limit curve for pure titanium sheet

Commercially pure titanium（CP Ti） has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformation characteristics and press formability of the CP Ti sheet are not much in comparison with automotive steels and aluminum alloys. The mechanical properties and hardening behavior evaluated in stress-strain relation of the CP Ti sheet are clarified in relation with press formability. The flow curve denoting true stress-true strain relation for CP Ti sheet is fitted well by the Kim-Tuan hardening equation rather than Voce and Swift models. The forming limit curve（FLC） of CP Ti sheet as a criterion for press formability was experimentally evaluated by punch stretching test and analytically predicted via Hora＇s modified maximum force criterion. The predicted FLC by adopting Kim-Tuan hardening model and appropriate yield function shows good correlation with the experimental results of punch stretching test.

GENERALIZED FATIGUE CONSTANT LIFE CURVE AND TWO-DIMENSIONAL PROBABILITY DISTRIBUTION OF FATIGUE LIMIT

According to the traditional fatigue constant life curve, the concept and the universal expression of the generalized fatigue constant life curve were proposed. Then, on the basis of the optimization method of the correlation coefficient, the parameter estimation formulas were induced and the generalized fatigue constant life curve with the reliability level p was given. From P-S-a-S-m curve, the two-dimensional probability distribution of the fatigue limit was derived. After then, three se, of tests of LY11 CZ corresponding to the different average stress were carried out in terms of the two-dimensional up-down method. Finally, the methods are used to analyze the test results, and it is found that the analyzed results with the high precision may be obtained.

LIMITS OF BERNSTEIN-BEZIER CURVES FOR PERIODIC CONTROLNETS

If n given control, points b_0,…b_(n-1)∈R^d are repeated periodically by b_(i+kn)=b_i, for all k∈Z. the uform limit of the Bernstein-Bezier polynomial curves of degree r with control points b_0,….b_ for r→∞ is a Poisson curve(after a suitable reparametrization). This fact reveals some interesting self-simi- lar structures in case of regular n-gons in the plane.

Expiratory Flow Limitation and Its Relation to Dyspnea and Lung Hyperinflation in Patients with Chronic Obstructive Pulmonary Disease: Analysis Using the Forced Expiratory Flow-Volume Curve and Critique

Background: Tidal expiratory flow limitation (tEFL) is defined as absence of increase in air flow during forced expiration compared to tidal breathing and is related to dyspnea at rest and minimal exertion in patients with chronic airflow limitation (CAL). Tidal EFL has not been expressed as a continuous variable (0% - 100%) in previous analyses. Objective: To relate the magnitude of tEFL to spirometric values and Modified Medical Research Council (MMRC) score and Asthma Control Test (ACT). Methods: Tidal EFL was computed as percent of the tidal volume (0% - 100%) spanned (intersected) by the forced expiratory-volume curve. Results: Of 353 patients screened, 192 (114 M, 78 F) patients (136 with COPD, 56 with asthma) had CAL. Overall characteristics: (mean ± SD) age 59 ± 11 years, BMI 28 ± 7, FVC (% pred) 85 ± 20, FEV1 (% pred) 66 ± 21, FEV1/FVC 55% ± 10%, RV (% pred) 147 ± 42. Tidal EFL in patients with tEFL was 53% ± 39%. Using univariate analysis, strongest correlations were between tEFL and FVC and between tEFL and RV in patients with BMI < 30 kg/m2. In patients with nonreversible CAL, tEFL was positively associated with increasing MMRC, negatively with spirometric measurements, and positively with RV/TLC. In asthmatics, ACT scores were higher in patients with mean BMI ≥ 28 kg/m2 (p < 0.00014) and RV/TLC values > 40% (p < 0.03). Conclusions: Dyspnea is strongly associated with tEFL and lung function, particularly in patients with nonreversible CAL. Air trapping and BMI contribute to tEFL.

NURBS CURVE INTERPOLATOR WITH ADAPTIVE ACCELERATION-DECELERATION CONTROL

The feedrate profile of non-uniform rational B-spline （NURBS） interpolation due to the contour errors is analyzed. A NURBS curve interpolator with adaptive acceleration-deceleration control is presented. In interpo- lation preprocessing, the sensitive zones of feedrate variations are processed with acceleration-deceleration control. By using the proposed algorithm, the machining accuracy is guaranteed and the feedrate is adaptively adjusted to he smoothed. The mechanical shock imposed in the servo system is avoided by the first and the second time derivatives of feedrates. A simulation of NURBS interpolation is given to demonstrate the validity and the effectiveness of the algorithm. The proposed interpolator can also be applied to the trajectory planning of the other parametric curves.

Research on Induction Normal Curvature and Critical Curves of Quasi－ellipsoidal Gear Drive with Inner－toroidal Teeth

Quasi-ellipsoidal gear drive is suitable for the precise flexible joint of robot,but some meshing problems of this transmission are rarely involved in the related papers.According to the two-parameter conjugate surface theory, this article studies on the induction normal curvature and critical curves, the method of analysis is efficient for not only the quasi-ellipsoidal gear drive but also the other types of spatial gear drive.

Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid

Investigated in this study is the flow induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.

Diffraction limit of light in curved space

Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures.With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years,how spatial curvature affects the diffraction limit is an attractive and important question.Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution(SORs)with constant or variable spatial curvature.We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature,opening a new avenue to super-resolution.The diffraction limit is also influenced by the propagation direction,as well as the propagation distance in curved space with variable spatial curvature.These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.

Limit equilibrium analysis for stability of soil nailed slope and optimum design of soil nailing parameters

Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.

LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE

In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola.For this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a center.For other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf bifurcation.This result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.

Existence of Limit Cycles for a Cubic Kolmogorov System with a Hyperbolic Solution

This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.

配电网分布式发电渗透率极限值定义与计算方法

未来配电网接入分布式发电的比例将不断提高,为此提出了分布式发电(distributed generation,DG)渗透率极限值的定义及计算方法。首先,利用消纳能力曲线和负荷时序特性得到按时间分布的消纳能力。其次,在此基础上定义功率、容量和能量3个渗透率极限值。将渗透率极限值定义为保证任一时刻DG出力不超过该时刻消纳能力下的渗透率的最大值。再次,给出渗透率极限值的计算方法。根据DG容量及其时序出力特性和按时间分布的消纳能力确定DG容量极限值,进而得到渗透率极限值。最后,用IEEE 33节点算例进行验证,与现有方法比较表明,所得结果更为准确。定义的渗透率极限值易于使用,在满足安全性前提下,为衡量DG接入配电网程度提供了重要的参考指标。

双色散-双聚焦X射线光谱仪研制与特性研究

X射线发射谱技术(XES)是一种原位无损获得元素化学形态的技术方法,目前国内外实验室型X射线发射谱测定装置的研制尚处于探索阶段。能量色散X射线荧光(EDXRF)光谱仪和波长色散X射线荧光(WDXRF)光谱仪在地质、环境、考古等多学科领域得到广泛应用,然而,EDXRF虽结构简单,可实现多元素快速无损检测,但分辨率不理想、谱线干扰严重,检出限较差;WDXRF虽可分辨常规应用中多数具有谱线重叠特性的元素,但结构复杂成本高。为探索实验室型XES装置研制,该研究综合了能量色散X射线荧光和波长色散X射线荧光的性能优势,提出了一种波长-能量双色散、激发-发射双聚焦X射线光谱仪(DDF-XRS)设计理念,并成功研制了原理样机。实验数据和分析结果显示,该DDF-XRS型光谱仪兼具聚焦X射线和波长与能量色散光谱仪的优点,结构简单,信噪比好,具有高分辨率和低检出限特性。通过波长-能量双色散技术,X射线首先被晶体衍射发生波长色散,从而获得单色光,同时利用硅漂移探测器的能量色散特性,降低谱线干扰误判风险,提高分析结果准确,该技术克服了WDXRF结构复杂和EDXRF能量分辨率不足的限制,凸显了双色散的必要性和优越性。目前DDF-XRS光谱仪分辨率45 eV,可减少过渡金属K_(β)对K_(α)峰的谱线重叠影响;同时,显著降低了连续谱背景,最优信噪比>1000;测定地质样品中的Cr,检出限可达0.26 mg·kg^(-1)。应用DDF-XRS,一定程度上已可分辨过渡金属K_(α1)和K_(α2)谱线,如结合线性或二维阵列探测器,则有望进一步提高分辨率,实现X射线发射指纹谱的测定,以获得分析元素的化学形态。由于目前的晶体特性尚不能达到完全分辨过渡金属的重叠谱线的性能要求,故探寻具有高分率能力、高衍射强度特性的弯晶,将成为下一步的研究重点。

不同加载条件下含瓦斯煤岩强度极限邻域范围研究

煤与瓦斯突出灾害的发生机理尚不清楚,据流变假说,含瓦斯煤岩在长期载荷下可能进入“强度极限邻域”,此时受外部冲击扰动更易破坏。为研究不同加载条件下含瓦斯煤岩的“强度极限邻域”,以找到进入该状态的影响规律,并建立相应的微观判别标准,利用自主研发的岩石流变扰动效应三轴试验系统和煤岩流变扰动效应渗流实验装置,开展不同围压、不同瓦斯压力、轴压下的含瓦斯煤岩流变扰动实验,通过核磁共振手段对流变扰动前后煤岩进行分析对比,得到不同加载条件下的孔隙率、孔径分布、T_(2)谱曲线。试验结果表明:①不同加载条件下的煤岩流变过程中,存在一个应力阈值,可以使得煤岩在受到外部冲击扰动后阈值左右邻域有不同力学性质的表现;当施加力小于此阈值时,冲击扰动后,煤岩的孔隙度减小,煤样随之被压缩紧密,T_(2)谱曲线中代表大孔径的谱峰降低,谱峰曲线左移;当施加力大于此阈值时,冲击扰动后,煤岩大孔径孔隙增多,T_(2)谱曲线出现右移,所有谱峰高度增大,说明该应力阈值是用来判断煤岩是否进入“强度极限邻域”关键。②围压和瓦斯压力对煤岩的影响具有相反的力学作用性质,在抗压能力、损伤程度、长期强度、“强度极限邻域”中有所表现,其中,围压越大,煤岩越晚进入“强度极限邻域”,瓦斯压力越大,煤岩则越早进入该邻域。③煤岩的孔径分布、T_(2)谱曲线能直观反映了煤岩“强度极限邻域”内、外微观变化特征。④通过煤岩孔隙率所确定的进入“强度极限邻域”时的轴压与围压、瓦斯压力构建函数方程可判断不同加载条件煤岩进入“强度极限邻域”的时机,作为进入“强度极限邻域”范围时的判别标准,其中围压越大,此时进入“强度极限邻域”范围时的应力阈值越大;瓦斯压力越大,进入“强度极限邻域”时的应力阈值越小。

STUDY ON THE UNIQUENESS OF LIMIT CYCLE OF THE QUADRATIC SYSTEM BY USING THE QUADRATIC CURVE WITHOUT CONTACT(CONTINUED 1)

In this paper, we continue to discuss the uniqueness of limit cycle of the quadratic system by using the quadratic curve without contact and several new criteria for the uniqueness have been obtained.

基于动态调节下垂曲线的光伏逆变器两阶段协调控制策略

在分布式光伏高渗透的有源配电网中,常规集中、局部电压控制已无法经济有效地解决电压越限、波动问题。为此提出光伏逆变器集中-局部电压两阶段控制策略,局部控制曲线采用多曲线节点灵活可调的改进无功-电压(Q-V)下垂曲线。集中控制阶段以电压控制成本与电压越限条件风险价值的加权和最小为目标函数,利用分布鲁棒优化算法和模型预测控制算法考虑光伏出力预测不确定性,对各光伏逆变器的有功功率削减量参考值和Q-V下垂曲线进行分钟级全局优化设置和调节;局部控制阶段根据Q-V下垂曲线和实时测量的节点电压,动态调整光伏逆变器无功出力。采用改进的IEEE 37节点配电系统进行仿真,结果表明:所提控制策略不仅能够集中、最优地协调各光伏逆变器的有功功率削减量和无功出力,避免电压越限,还能在局部控制阶段利用集中优化后的Q-V下垂曲线使电压波动降低40.56%,满足配电网运营商对电压控制经济性和鲁棒性的不同需求。