MATHEMATICAL EXPECTATION ABOUT DISCRETE RANDOM VARIABLE WITH INTERVAL PROBABILITY OR FUZZY PROBABILITY

IntroductionFor the continuous second kind RVFP,namely,the continuous random variable withcrisp event-fuzzy probability,the basic concepts/definitions and calculating methods of thefuzzy probability density function,the random variable with fuzzy density …     

Theory of fuzzy random vibration with fuzzy parameters

In this paper, based on our previous papers [1–4], the general theory of fuzzy random vibration with fuzzy parameters is studied. In order to better describe the random excitation with fuzziness in mathematics, first, the random variable and random process with a fuzzy parameter are defined and their probability distributions and statistical moments are discussed. Secondly, by simulating the fuzzy random excitation as a random process with a fuzzy parameter, the fundamental method and numerical method are presented for analysing the fuzzy random response of linear or nonlinear oscillators subjected to this kind of excitation. Finally, the methods are applied to the fuzzy random vibration of aseismic structures and a concrete example is given.This paper is supported by the Natural Science Foundation of China.     

RANDOM VARIABLE WITH FUZZY PROBABILITY

IntroductionThematteroffuzzyrandomisusuallyclassifiedintothreeparts:fuzzyevent_exactitudeprobabilitymodel,crispevent_fuzzyprobabilitymodel,fuzzyevent_fuzzyprobabilitymodel.Uptonow ,themajorityofresearchesandachievementsareaboutthefirstmodel,buttherearefewresearchesandachievementsaboutthesecondmodel[1- 4].Whenresearchingthesecondmodel,thefuzzyprobabilityaboutcertainbasiceventsmustbegivenfirst,andthefuzzinessofvariablesiscausedbythefuzzyprobabilityaboutthesebasicevents.Theabove_mentionedrelation…     

基于马尔科夫链与鞍点逼近的模糊随机可靠性分析方法

针对同时存在随机不确定性和模糊不确定性的可靠性分析问题,提出了两种高效解决方法。一种是迭代马尔科夫链鞍点逼近法,该方法的基本思想是给定隶属水平下由迭代马尔科夫链和一次鞍点逼近法求得可靠度上下限,不同的隶属水平对应不同的可靠度上下限,遍历隶属水平的取值区间[0,1]即可求得可靠度隶属函数,与传统的两相Monte Carlo数字模拟法和迭代一次二阶矩法相比,该方法具有效率高和对非正态基本随机变量不需要进行正态转换的优点;第二种方法是迭代条件概率马尔科夫链模拟法,该方法在求解给定隶属度水平下的可靠度上下限时,由条件概率公式引入一个非线性修正因子,该因子的引入大大提高了功能函数为非线性的可靠性问题的求解精度。本文算例验证了所提方法的优越性。     

平稳随机激励下随机桁架结构动力可靠性分析

研究了随机桁架结构在平稳随机激励下的动力可靠度求解方法。同时考虑结构物理参数、几何尺寸的随机性,利用求解随机变量数字特征的代数综合法和矩法,从结构随机响应的频域表达式出发,导出了随机桁架结构在平稳随机激励下的位移、应力及其导数响应均方值的数字特征,再由动力可靠性的Poisson公式导出了结构动力可靠度的计算公式。通过算例分析了各参数的随机性对结构动力可靠度的影响,验证了该方法的可行性和有效性。     

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY- STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices are constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic are then derived by using the random variable's moment function method and algebra synthesis method. Two examples are used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.     

半主动TLCD对偏心结构的离散模糊变结构控制

采用在结构水平双向设置TLCD半主动控制装置的方法,对偏心结构在多维地震作用下的离散模糊变结构控制问题进行了研究.首先建立了结构-TLCD扭转耦联控制系统微分方程及其离散化状态空间表达,然后阐述了基于模糊逻辑的变结构控制的基本策略,最后应用该模糊变结构控制策略对一个五层偏心结构的TLCD半主动控制问题进行了仿真分析.仿真分析的结果表明,该方法在对结构的平动反应和扭转反应都能起到较好的减震效果的同时,还具有对结构固有参数不确定性的较强的鲁棒性.     

1‐D numerical modelling of shallow flows with variable horizontal density

A1‐D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth‐averaged mass and momentum conservation of a liquid–species mixture, and mass conservation of the species in the horizontal direction. Here, the term ‘species’ refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper‐concentrated sediment‐laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov‐type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable‐density flows, where analytical steady‐state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non‐uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright © 2009 John Wiley & Sons, Ltd.     

Post-buckling of a cantilever rod with variable cross-sections under combined load

IntroductionSinceEuler[1] ,Lagrange[2 ] ,Love[3 ] etal.investigatedtheslenderrod ,asoneofthebasicstructuralstabilityproblems ,manyattentionshavebeenpaidtothepost_bucklingofelasticrodsforalongtime .Today ,flexiblerodshavebeenwidelyusedasspring ,linkages ,robot’sarms,largeantennasandsoon .Hence ,thestudiesofpost_bucklingofelasticrodshavewideengineeringandapplyingbackgroundsinrecentdays .Basedontheassumptionthattheaxiallineoftherodisinextensible ,Timoshenkoetal.[4] examinedthepost_bucklingofco…     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

可伸长变截面杆的弹性过屈曲模型及其数值解

在Ｋｉｒｃｈｈｏｆｆ基本假设下,基于轴线可伸长弹性杆的几何非线性理论,建立了一端简支另一端固定夹紧变截面直什的过屈曲控制方程,并应用打靶法直接数值求解相应的强非线性过值问题,获得了数值意义上的精确解。     

任意变厚度的旋转扁薄壳非线性稳定的幂函数解法

以幂函数为试函数,两次使用配点法成功地分离了耦合的大挠度方程,从而导出变厚度旋转扁壳非线性稳定的计算式。支座可以是弹性的。本文给出了均布或多项式分布荷载作用下,线性或多项式型变厚度的圆锥壳、球壳、余弦壳或四次多项式型旋转壳的上、下临界荷载。均布荷载作用下指数型变厚度球壳的上临界荷载同其他方法的结果作了比较。用配点法编写的程序具有收敛范围大、精度高、通用性强和计算时间少的优点。     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of shooting methods for two-point boundary value problems of ordinary differential equations with parameters in hydrodynamics

In this paper. first we introduce the shooting method (including the method of adjoints and the method of quasilinearization) for two-point boundary value problems of ordinary differential equations with parameters, and give out an example of solving hydrodynamic lubrication equation by using the shooting method. The calculated results are satisfactory.     

Peristaltic transport and heat transfer of a MHD Newtonian fluid with variable viscosity

The influence of temperature‐dependent viscosity and magnetic field on the peristaltic flow of an incompressible, viscous Newtonian fluid is investigated. The governing equations are derived under the assumptions of long wavelength approximation. A regular perturbation expansion method is used to obtain the analytical solutions for the velocity and temperature fields. The expressions for the pressure rise, friction force and the relation between the flow rate and pressure gradient are obtain. In addition to analytical solutions, numerical results are also computed and compared with the analytical results with good agreement. The results are plotted for different values of variable viscosity parameter β, Hartmann number M, and amplitude ratio ?. It is found that the pressure rise decreases as the viscosity parameter β increases and it increases as the Hartmann number M increases. Finally, the maximum pressure rise (σ=0) increases as M increases and β decreases. Copyright © 2009 John Wiley & Sons, Ltd.     

平稳随机振动荷载识别的逆虚拟激励法（一）

本文将虚拟激励法作了逆向推广，从而用确定性方式求解了平稳随机振动的荷载谱识别问题。即已知部分响应的自谱与互谱，反求多点激励间的自谱与互谱。并通过计算机模拟，讨论了识别的精度及影响因素等问题。     

平稳随机振动荷载识别的逆虚拟激励法（二）

本文将逆虚拟激励法（ＩＰＥＭ）用于求解平稳随机振动的荷载谱识别问题，已知部分结构应变（或部分应变及部分位移）响应的自谱与互谱，反求多点激励间的自谱与互谱。     

具有大量椭圆随机分布区域的数值模拟及应用

利用椭圆的参数方程,首先给出平面上的点位于椭圆内部与外部的判别条件,再把计算点到椭圆距离问题,化为一个求最值问题,使得可以用搜索法较快地得到有效的近似解,从而得到一个新的产生具有大量椭圆随机分布区域的方法,基本思想是：（1） 对于模拟区域内随机生成的点,先判断该点是否在所有已生成椭圆的外部,若是,计算它与所有已生成椭圆边界的距离;（2） 如果所求的距离大于或等于欲生成的椭圆的长半轴,则以该点为中心,生成一个新的椭圆。这样,不必用一个多边形覆盖来判别椭圆之间是否相交或重叠,可以使生成的椭圆与椭圆之间的距离更小一些（甚至可以是零）,从而提高了模拟区域中椭圆的密度。试验表明,针对混凝土,可以在比较短的时间内,按3级配生成骨料含量可高达70%以上的模拟试件,按2级配生成骨料含量可高达60%以上的模拟试件。对所生成的混凝土试件,做了简单的加载力学实验。计算结果表明,该方法生成的模型能够满足力学分析的需要;进一步,基于椭圆随机分布区域,使用椭圆作为覆盖,建立了高含量的参数化不规则骨料模型试件。     

A NEW SOLUTION TO STRUCTURAL FUZZY FINITE ELEMENT EQUILIBRIUM EQUATIONS (SFFEEE)

I.IntroductionInthefieldofthefuzzyfiniteelementmethod(FFEM),tostudynow,tosolvetheequilibriumequationsisofmomentoussignificance.EspeciallyfortheapplicationoftheFFEMtoengineeringproblems,thekeyworktodoistoexplorehigh-speedandhigh-effeciencysolutionstoequili…     

SIMPLE‐H: a finite‐volume pressure–enthalpy coupling scheme for flows with variable density

We present a method that simultaneously solves the pressure‐correction equation and the energy equation in a conventional SIMPLE scheme. In comparison to other techniques, the new method leads to a remarkable reduction in the number of required iterations, in particular for problems characterized by significant temperature gradients. It is shown that this translates to very attractive computing times. Copyright © 2011 John Wiley & Sons, Ltd.