Fully coupled flow-induced vibration of structures under small deformation with GMRES method

Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual （GMRES） method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.     

弹性地基上矩形加肋板自由振动分析的无网格法

应用移动最小二乘无网格法研究弹性地基上矩形加肋板的自由振动问题。假设弹性地基与加肋板紧密接触,以弹簧模拟弹性地基,将弹性地基上的加肋板视为板与肋条组合的结构。基于一阶剪切理论,用无网格伽辽金法推出了板和肋条各自的动能与势能;再通过位移协调条件将两者的能量叠加,得到了弹性地基上整个加肋板的动能与势能。由Hamilton原理导出了弹性地基上加肋板自由振动的控制方程。采用完全转换法引入边界条件,求解自由振动方程,并编制了计算程序,给出了算例。将算例与ABAQUS有限元解及已有文献结果进行了比较分析,其相对误差均在5%以内,验证了该方法计算弹性地基上矩形加肋板结构自振频率的有效性。     

三角形格构式塔身体型系数及屏蔽特性研究Study on shape coefficient and shielding effects of triangular latticed tower body

为满足高压／特高压输电铁塔风致倒塌问题对铁塔体型系数的精准度需求,研究了完全结构化多块网格对格构式三角形输电塔塔身流场的模拟能力,探讨了不同规范体型系数对某铁塔的适用性,并分析了塔身杆件复杂流动干扰作用下的屏蔽特性。结果表明,数值模拟与风洞试验的体型系数吻合很好;完全结构化网格能高保真、高度正交地对铁塔塔身这类复杂空间桁架流场进行离散;《英国杆塔荷载规范》的规定结果虽偏于保守,但其趋势最为接近真实值;在塔身桁架结构各个杆件之间流动干扰作用下,角钢弯折角朝向来流比背向来流的屏蔽作用更强;斜材弯折角背向气流和竖向辅助材弯折角朝向气流的组合之间的流动干扰,使得其对气流的屏蔽作用最强。     

线弹性体本构方程对称性的逆命题研究

基于线弹性体本构方程系数矩阵的对称性,提出了其对应的逆命题问题,即若材料本构方程是线性且对称的,能否由此确定物体是完全弹性的?论文通过构造势函数的方法对该问题给出了肯定的回答,从而论证了对于符合线性本构关系的材料,其本构方程的对称性与物体的完全弹性相互蕴含,因而是相互等价的.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

关于3—正则子图问题的一个注记

这篇注记证明判断一个图是否有３－正则子图的问题，即使对于节点次不超过４的平面力，仍然是ＮＰ－完全的，而且，此结果是最好的可能。     

具有不完全信息的多重支付二人零和对策问题

本文研究多品性支付的二人零和对策问题,其中局中人可利用的信息是不完全的。同时假定局中人1并不知道各支付矩阵的数值,而只是对各支付品性在各自然状态下把局势的后果排出倾向上的次序。对于给定的置信水平,引进了权序上限和权序下限的概念,进而引出有效策略的概念。通过一系列的推导,给出了求最优策略的近似算法。     

有耗介质完全匹配层在时域多分辨分析中的应用

对无耗和有耗介质中的完全匹配问题进行了研究,将广义完全匹配吸收层(GPML)应用到时域多分辨分析（MRTD）中。GPML是在扩展坐标系下由Maxwell方程得到的,在MRTD中实现对GPML的求解,并在频域对GPML进行了有效性分析,得出了GPML在不同空间步长和不同吸收层厚度情况下入射波由真空入射到吸收层的反射系数在频域的分布,并给出了有耗介质中GPML吸收效果的例子。结果表明,GPML的反射系数在一定频率范围内小于-40 dB,且随着计算空间步长的减小和吸收层厚度的增加而减小。GPML既可以用来截断无耗介质也可以用来截断有耗介质,为时域多分辨分析方法提供了一种较为通用的吸收边界。