A hybrid/mixed model finite element analysis for eigenvalue problem of moderately thick plates

The buckling and free vibration problems of moderately thick plate are considered in this paper by using the hybrid/mixed finite element model. A modified Reissner principle which only requires C⁰ continuity is derived. No lockling phenomenon is observed. Linear interpolation is used for all independent unknown function. Finally a displacement generalized eigenvalue equation is obtained, in which the stiffness matrix is symmetric and positively definite. The calculated results show that the method proposed is simple, reliable and satisfactory.     

岩土工程中的位移反分析法

从弹性力学的位移基本方程出发，讨论了平面应变情况下的各类反演问题，扩展了文［１］的结果，并研制出相应的软件，最后给出的算例表明了算法的可行性及计算精度。     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

微分方程反问题的梯度正则化法

本文在微分方程反问题研究当前发展状况的基础上,提出了一种求解微分方程反问题的比较统一的方法——梯度正则化法。该方法将反问题的求解分为两个主要部分,一是展开以求补充条件对未知参数的梯度矩阵,二是正则化以解不适定的线性方程组。梯度正则化法从反问题的共性入手,未附加任何特殊的约束,所以可以适用各种类型的反问题,且在求解时不受空间维数的限制。     

高层建筑风荷载反演研究

本文研究了结构参数未知条件下的高层建筑风荷载反演问题,通过将平均风速的实测特性作为识别计算中的辅助条件,文中提出了一类荷载归一化统计平均方法,结合工程实例,进行了高层建筑风荷载反演分析,结果表明,本文建议方法可以在幅值、时程等方面均给出良好的风荷载反演结果,同时识别得到的结构参数具有良好的精度。从而为高层建筑风荷载研究提供了一条可行途径。     

A simulated annealing-based inverse computational fluid dynamics model for unknown parameter estimation in fluid flow problem

In this paper, a simulated annealing (SA)-based optimisation is carried out for simultaneous estimation of the Reynolds number (Re) and the dimensions of the enclosure (l_x, l_y ) from the knowledge of centreline velocity field. For demonstrating the retrieval methodology, the required centreline velocity field is first obtained from a forward method using some known values of the unknowns, which are ultimately estimated by the inverse method. SA is used to optimise the objective function represented by the square of the difference between the known field and an arbitrary guessed field (calculated using some guessed value of the unknowns). For studying the sensitivity of the estimated parameters, the effect of random errors has been investigated and the suitability of the SA has been checked for different initial guesses. The algorithm reported in the present work is useful in estimating the above unknowns (Re, l_x, l_y ) for a given velocity field.     

粗糙表面之间接触热阻反问题研究

当两个固体表面相互接触时,由于接触面粗糙度的影响,界面间就形成了非一致接触,这种接触导致热流收缩,进而产生接触热阻. 目前的理论研究主要集中在正问题研究,对反问题的研究相对较少. 接触热阻反问题研究是通过研究部分边界温度、热流和部分测量点的温度来反演得到界面上的接触热阻. 反问题研究在很多工程领域都有应用,如航空航天、机械制造、微电子等,是工程中确定接触热阻一种快速有效的方法. 本文采用边界元法和共轭梯度法研究了二维空间随坐标变化的接触热阻反问题. 为了验证方法的准确性和可行性,假定在已知部分测量点温度和真实接触热阻的情况下,反演计算得到界面的温度和热流,进而得到接触热阻,并与真实接触热阻进行比较. 结果表明采用边界元法和共轭梯度法在无测量误差的情况下,可以准确反演获得界面的真实接触热阻. 若存在测量误差,反演计算结果对测量误差极其敏感,反演结果误差会由于测量误差的引入而被放大. 为处理这种不适定性, 采用最小二乘法对反演计算结果进行校正,结果表明采用最小二乘法能够避开反问题中一些偏离实际值较大的测量点,显著提高反演计算结果的准确性.      

逆迭代法的一种变通应用

本文利用逆迭代法与共轭梯度法配合使用时的“广义力”一致出现之规律,将大型结构动力分析的有限元(条)网格以族排列,然后将单元族分批集于“广义力”向量之中,从而避开了传统的结构刚度阵与质量阵的集成过程,大大节约了计算机内存。整个过程极为简明、有效。     

A FE‐based algorithm for the inverse natural convection problem

Several numerical algorithms for solving inverse natural convection problems are revisited and studied. Our aim is to identify the unknown strength of a time‐varying heat source via a set of coupled nonlinear partial differential equations obtained by the so‐called finite element consistent splitting scheme (CSS) in order to get a good approximation of the unknown heat source from both the measured data and model results, by minimizing a functional that measures discrepancies between model and measured data. Viewed as an optimization problem, the solutions are obtained by means of the conjugate gradient method. A second‐order CSS in time involving the direct problem, the adjoint problem, the sensitivity problem and a system of sensitivity functions is used in order to enhance the numerical accuracy obtained for the unknown heat source function. A spatial discretization of all field equations is implemented using equal‐order and mixed finite element methods. Numerical experiments validate the proposed optimization algorithms that are in good agreement with the existing results. Copyright © 2010 John Wiley & Sons, Ltd.     

内爆法制备双金属管复合参数的计算机辅助设计

根据爆炸复合窗口理论和内爆轰作用下管的飞行姿态计算公式,编制计算机程序来确定双金属管内爆复合的工艺参数,使得复合参数的选取大为简化。结果表明,该方法可以用于指导内爆法制备双金属管复合工艺参数的选择。     

弹性、热弹性物性值反问题的边界元分析

本文采用边界元法和卡尔曼滤波,对弹性、热弹性问题物性值进行反分析,由有限个观测点的位移值,同时反算出材料的拉压弹性模量Ε、泊桑比ν和线膨胀系数α。     

Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe — Evolution of wall concentration

Summary In this paper, we are presenting a model of the evolution of the wall concentration of a macromolecular solution (PEO) annularly injected in a cylindrical pipe in a turbulent flow. This model valid for all diffusion zones is based on mathematical and physical considerations and proves to be in good agreement with the experimental data.

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Zusammenfassung Es wird ein Modell der Entwicklung der Wandkonzentration einer makromolekularen Lösung (PÄO) vorgestellt, die in einem wandnahen Ringspalt in die turbulente Strömung durch ein zylindrisches Rohr injiziert worden ist. Dieses für alle Diffusionszonen gültige Modell basiert auf mathematischen und physikalischen Betrachtungen und erweist sich für die Beschreibung der experimentellen Daten als gut geeignet.

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C _w wall concentration - C _i initial concentration before injection - L ₀ distance from the slot at which the wall concentration drops toe ^-1 of its original value - L _IT ,L _IF ,L _F characteristic lengths - L _I length scale of the second region - x downstream distance from the source - n _I ,n _T ,n _F characteristic exponents - K ₀,K _I ,K _F characteristic constants - ln natural logarithm - q _i flow rate of injection - Q _T flow rate - C _j =C _{i · q i} /Q _T concentration in homogeneous medium - A, B, C, m constants - p andq annex variables - Re Reynolds number With 7 figures     

平面结构可靠性预测的随机边界元逆分析法

在结构可靠性计算的随机边界元理论和逆分析法基础上,用随机边界元方程结合改进的卡尔曼滤波算法来预测结构的可靠性,提出了用于平面机械结构可靠性预测的边界元逆分析法理论;并将方法应用于同时存在未知缺陷和随机边界载荷模型,进行了结构可靠性预测,在识别缺陷的同时预测出随机边界载荷的分布参数及结构体上各点的结构可靠度指标,给出了平面结构模型的数值示例。     

Two‐objective optimization strategies using the adjoint method and game theory in inverse natural convection problems

This paper considers the problem of estimating the strengths of two time‐varying heat sources simultaneously, from measurements of the temperature inside the square domain in a porous medium, when prior knowledge of the source functions is not available. This problem is an inverse natural convection problem. In order to circumvent this problem, we define several optimization criteria (objective functionals) that measure discrepancies between model and measured data, where objective functionals depend on two heat sources and use multi‐criteria optimization to identify Nash equilibria, which are solutions to the non‐cooperative game according to game theory. Two non‐cooperative game strategies are considered: competitive (Nash) game and hierarchical (modified Stackelberg) game. The methodology that we employ relies on a combination of mixed finite element space approximations, finite difference time discretizations, adjoint equation and sensitivity equation techniques, and nonlinear conjugate gradient algorithms for the solutions of estimating two heat sources. Applying the Sobolev gradient for the noise removal is investigated. The performance of the present technique of inverse analysis is evaluated, by means of several numerical experiments, and is found to be very accurate as well as efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

应用变域变分有限元法解平面叶栅反命题

反命题作为一种可变(未知)边界问题近年来得到了广泛的研究。本文给出了亚声速平面叶栅反命题计算的势函数变域变分有限元解法。变域变分通过把可变边界结合在变分泛函中，使其与求解流场的控制方程结合起来，从而使可变边界求解和流场分析可以完全耦合进行。本文针对亚声速平面叶栅的反命题，根据泛函的驻值必要条件，介绍了变域变分有限元方法的求解过程，最后给出了两个数值算例。这两个算例均采用四节点矩形单元的插值基函数，第一个算例用于检验程序的可靠性，第二个算例设计了一个给定叶面马赫数分布的叶型，并与试验结果进行对照。     

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。     

CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM

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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。     

流体力学反命题变分有限元非线性规划法

本文在用有限元法求解变域问题时，利用变域变分公式将问题化为求泛函的驻值，但该驻值常常是一个鞍点，因此给计算带来不便，我们在这里利用最小二乘法将求驻值的问题转化为求另一泛函的极值问题，然后采用LMF方法和共轭梯度法求解极值问题。     

Solution of the Inverse Boundary Value Problem of Aerohydrodynamics for a Two-Element Airfoil

The basic inverse boundary value problem of aerohydrodynamics for a two-element airfoil is analytically and numerically solved in the complete formulation. The problems of designing biplane airfoils and an airfoil with a trailing-edge flap or leading edge flap (slat) are solved for a given distribution over the unknown contours of the velocity or the pressure as a function of the contour arc abscissa of the airfoils which depends on a finite number of the parameters.