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The CDF and its sensitivity analysis of stochastic structure with stochastic excitation by advanced stratified line sampling

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Science China(Physics,Mechanics & Astronomy) 2013年第8期56卷 1559-1567页

作者： SONG ShuFang LU ZhenZhou ZHANG WeiWeiNational Key Laboratory of Aerodynamic Design and Research northwestern polytechnical university YE ZhengYin School of Aeronautics Northwestern Polytechnical University National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University

For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).

关键词： stochastic excitation line sampling cumulative distribution function (CDF) sensitivity analysis root bending moment (RBM) gust response analysis

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Behavior of Growth and Coarsening of T_1(Al_2CuLi) Precipitates in Al-Li Alloys 2090 and 2090+Ce

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Rare Metals 2001年第3期20卷 174-177页

作者： Zhilong Zhao, Lin Liu, Zheng Chen Dopartment of Mechanical Engineering, northwestern polytechnical university, Xi’an 710072, China 西北工业大学陕西西安 710072

The behavior of growth and coarsening of T-1(Al2CuLi) precipitates was comparatively studied by means of TEM technique in two Al-Li alloys 2090 and 2090+Ce (with cerium content less than 0.1% in mass fraction). Statistical analysis results show that T-1 precipitates in alloy 2090+Ce have smaller aspect ratio, which is connected with the more intersections between different T-1 variants in this alloy. It is also found that the variation of maximum length of T-1 precipitates with aging time can be obviously divided into two stages of growth and coarsening. The diffusion coefficients of solute atoms of Cu and Li are calculated via growth kinetics curves of T-1 precipitates. The results show that the diffusion of atom Cu plays a more important role in the formation of T-1 precipitates.

关键词： Al-Li alloy T-1(Al2CuLi) precipitates growth and coarsening trace addition of cerium

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Saddlepoint approximation based line sampling method for uncertainty propagation in fuzzy and random reliability analysis

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Science China(Technological Sciences) 2010年第8期53卷 2252-2260页

作者： LI LuYi,LU ZhenZhou &SONG ShuFang School of Aeronautics,northwestern polytechnical university,Xi’an 710072,China School of Aeronautics Northwestern Polytechnical University

For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation(SA)based line sampling *** the presented method,the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership *** the value domain of the fuzzy basic variables corresponding to the given membership level,bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random *** this way the uncertainty of the basic variables is propagated to the safety measurement of the structure,and the fuzzy membership function of the reliability is *** to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables,the presented method can considerably improve computational efficiency with acceptable *** presented method has wider applicability compared to the transformation method,because it doesn't limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing ***,the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable,which isn't suitably approximated by the existing transformation *** examples are provided to illustrate the advantages of the presented method.

关键词： membership function fuzzy reliability fuzzy variable random variable saddlepoint approximation based line sampling method

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THE STUDY OF THE GLOBAL STABILITY OF HIGH PERFORMANCE AIRCRAFT AT HIGH ANGLES-OF-ATTACK

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Chinese Journal of Aeronautics 1989年第2期 87-101页

作者： Gao Hao and Zhou Zhiqiang northwestern polytechnical university

In order to study the global stability of the high performance aircraft at highangles-of-attack,this paper describes a new approach based on the qualitativetheory of O.D.E,bifurcation analysis and catastrophe ***,a series ofalgorithms is given,by which equilibrium,bifurcation surfaces and periodicattractors are calculated and the global stability of the aircraft is ***,the relations between the stability criteria commonly used in aircraftdesigns and the eigenvalues of linearized matrices at the equilibrium points ***,by means of calculation of a concrete aircraft,some importanthigh angles-of-attack flight phenomena,such as jump,hysteresis,wing rockand spin are analysed by the approach.

关键词： AT high

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Digital image processing of sectorial oscillations for acoustically levitated drops and surface tension measurement

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Science China(Physics,Mechanics & Astronomy) 2010年第12期53卷 2260-2265页

作者： SHEN ChangLe, XIE WenJun & WEI BingBo Department of Applied Physics, northwestern polytechnical university, Xi’an 710072, China northwestern polytechnical university Department of Applied Physics Xi’an China (GRID:grid.440588.5) (ISNI:***)

A type of non-axisymmetric oscillations of acoustically levitated drops is excited by modulating the ultrasound field at proper frequencies. These oscillations are recorded by a high speed camera and analyzed with a digital image processing method. They are demonstrated to be the third mode sectorial oscillations, and their frequencies are found to decrease with the increase of equatorial radius of the drops, which can be described by a modified Rayleigh equation. These oscillations decay exponentially after the cessation of ultrasound field modulation. The decaying rates agree reasonably with Lamb’s prediction. The rotating rate of the drops accompanying the shape oscillations is found to be less than 1.5 rounds per second. The surface tension of aqueous ethanol has been measured according to the modified Rayleigh equation. The results agree well with previous reports, which demonstrates the possible application of this kind of sectorial oscillations in noncontact measurement of liquid surface tension.

关键词： acoustic levitation drop oscillation image processing surface tension

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Phase separation and rapid solidification of liquid Cu_(60)Fe_(30)Co_(10) ternary peritectic alloy

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Science China(Physics,Mechanics & Astronomy) 2007年第4期50卷 509-518页

作者： DAI FuPing, CAO ChongDe & WEI BingBo Department of Applied Physics, northwestern polytechnical university, Xi’an 710072, China Department of Applied Physics Northwestern Polytechnical University

The metastable liquid phase separation and rapid solidification of Cu60Fe30Co10 ternary peritectic alloy were investigated by using the drop tube technique and the differential scanning calorimetry method. It was found that the critical temperature of metastable liquid phase separation in this alloy is 1623.5 K, and the two sepa- rated liquid phases solidify as Cu(Fe,Co) and Fe(Cu,Co) solid solutions, respec- tively. The undercooling and cooling rate of droplets processed in the drop tube increase with the decrease of their diameters. During the drop tube processing, the structural morphologies of undercooled droplets are strongly dependent on the cooling rate. With the increase of the cooling rate, Fe(Cu,Co) spheres are refined greatly and become uniformly dispersed in the Cu-rich matrix. The calculations of Marangoni migration velocity (VM) and Stokes motion velocity (VS) of Fe(Cu,Co) droplets indicated that Marangoni migration contributes more to the coarsening and congregation of the minor phase during free fall. At the same undercooling, the VM/VS ratio increases drastically as Fe(Cu,Co) droplet size decreases. On the other hand, a larger undercooling tends to increase the VM/VS value for Fe(Cu,Co) drop- lets with the same size.

关键词： ternary peritectic alloy metastable immiscibility rapid solidification reduced gravity liquid phase separation

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Moment-independent importance measure of basic random variable and its probability density evolution solution

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Science China(Technological Sciences) 2010年第4期53卷 1138-1145页

作者： CUI LiJie,Lü ZhenZhou & ZHAO XinPan School of Aeronautics,northwestern polytechnical university,Xi’an 710072,China School of Aeronautics Northwestern Polytechnical University

To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and *** on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the *** use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance *** numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the *** results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic ***,the results show that the established solution on the probability density evolution is efficient for the importance measures.

关键词： basic random variable moment-independent importance measure probability density evolution method

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Conditional probability Markov chain simulation based reliability analysis method for nonnormal variables

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Science China(Technological Sciences) 2010年第5期53卷 1434-1441页

作者： YUAN XiuKai,LU ZhenZhou & QIAO HongWei School of Aeronautics,northwestern polytechnical university,Xi’an 710072,China School of Aeronautics Northwestern Polytechnical University

Based on fast Markov chain simulation for generating the samples distributed in failure region and saddlepoint approximation(SA) technique,an efficient reliability analysis method is presented to evaluate the small failure probability of non-linear limit state function(LSF) with non-normal *** the presented method,the failure probability of the non-linear LSF is transformed into a product of the failure probability of the introduced linear LSF and a feature ratio *** introduced linear LSF which approximately has the same maximum likelihood points as the non-linear LSF is constructed and its failure probability can be calculated by SA *** feature ratio factor,which can be evaluated on the basis of multiplicative rule of probability,exhibits the relation between the failure probability of the non-linear LSF and that of the linear LSF,and it can be fast computed by utilizing the Markov chain algorithm to directly simulate the samples distributed in the failure regions of the non-linear LSF and those of the linear ***,the expectation and variance of the failure probability estimate are *** results of several examples demonstrate that the presented method has wide applicability,can be easily implemented,and possesses high precision and high efficiency.

关键词： reliability failure probability Markov chain Monte Carlo

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Transition from Metastablity to Instability in Dynamics for the Precipitation of δ'(Al_3Li)

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Rare Metals 2001年第4期20卷 240-247页

作者： Xiaoling Li, Zheng Chen, Bing Liu, Yongxin Wang Department of Materials Science and Engineering, northwestern polytechnical university. Xi’an, 710072, China 西北工业大学陕西西安 710072

A computer simulation study on dynamics for the precipitation of δ'(Al_3Li) ordered particles from a disor- dered matrix (α) in binary Al-Li alloys is performed using the microscopic Langevin equation. A unique precipitation mechanism is found near the ordering spinodal line. Different from the classical nucleation mechanism in the me- tastable region and the congruent ordering followed by spinodal decomposition in the instable region, a nonstoichi- ometric single ordered phase with composition fluctuations is formed by non-classical nucleation, and this ordered phase decomposes spinodally. It can be concluded that the precipitation dynamics of δ' phase from metastability to instability is gradual, and no sharp transition occurs near the mean-field spinodal line as the mean-field theory pre- dicts.

关键词： δ'(Al_3Li) precipitation dynamics non-classical nucleation gradual transition

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Role of Friction in Cold Ring Rolling

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Journal of Materials Science & Technology 2005年第6期21卷 914-920页

作者： He YANG+, Lianggang GUO and Mei ZHAN College of Materials Science and Engineering, northwestern polytechnical university, Xi’an 710072, China College of Materials Science and Engineering Northwestern Polytechnical University Xi'an 710072 China

Cold ring rolling is an advanced but complex metal forming process under coupled effects with multi-factors, such as geometry sizes of rolls and ring blank, material, forming process parameters and friction, etc. Among these factors, friction between rolls and ring blank plays an important role in keeping the stable forming of cold ring rolling. An analytical method was firstly presented for proximately determining the critical friction coefficient of stable forming and then a method was proposed to determine the critical friction coefficient by combining analytical method with numerical simulation. And the influence of friction coefficient on the quality of end-plane and side spread of ring,rolling force, rolling moment and metal flow characteristic in the cold ring rolling process have been explored using the three dimensional （3D） numerical simulation based on the elastic-plastic dynamic finite element method （FEM） under the ABAQUS software environment, and the results show that increasing the friction on the contact surfaces between rolls and ring blank is useful not only for improving the stability of cold ring rolling but also for improving the geometry and dimension precision of deformed ring.

关键词： Cold ring rolling Friction Elastic-plastic dynamic explicit FEM ABAQUS

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