通用有限元系统实现无限域波动仿真方法

在有限元模型中加入人工边界,可以进行无限域波动仿真。本文将介绍一种改进的Higdon人工边界,并通过适当的变换形式,将其在通用有限元软件上实现。最后通过数值实验验证了这种方法具有良好的稳定性和计算精度,并且实施简单方便,其他人工边界条件可参照本文方法,通过变换形式在通用有限元程序中实现。     

Flow Asymptotics of a Viscous Compressible Fluid with Discontinuous Initial Data

Asymptotics of a continuous solution to a plane problem on the motion of a viscous incompressible fluid with discontinuous initial velocity and pressure fields is studied by the boundarylayer method with simultaneous stretching of space and time coordinates.     

具有自由边的复合材料层合板的解析解

从三维弹性力学基本方程出发,通过假设自由边的边界位移函数,建立了正交异性层合板的状态方程,给出了对边自由,对边简支矩形板的解析解.此解满足层合板的基本方程和层间连续条件.用本文的方法比较容易处理层合板的自由边.算例表明,数值结果具有较高的精度.     

LocalC α convergence of elliptic regularizations of parabolic equations

The solutions of elliptic regularizations of the heat equation converge to the solutions of the corresponding evolution equation in weak energy norms. The technique is of relevance in control theory as well as variational inequalities. We show that the convergence actually takes place in some Hölder space. The result holds for a class of parabolic equations in divergence form and sufficiently integrable forcing terms.

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Sommario Le soluzioni delle regolarizzanti ellittiche dell'equazione del calore, convergono alle soluzioni della corrispondente equazione di evoluzione in norme deboli dell'energia. Questa tecnica trova applicazione nelle teoric dei controlli e disuguaglianze variazionali. Si dimostra che la convergenza é forte ed ha luogo in norme Hölderiane. Il risultato si estende ad una classe di equazioni paraboliche in forma di divergenza con termini forzanti sufficientemente integrabili.

     

Acoustic Radiation from a Finite Length Cylindrical Shell Excited by an Internal Acoustic Source: Solution Based on a Boundary Element Method and a Matched Asymptotic Expansion

This paper deals with acoustic radiation by a thin elastic shell, closed by two perfectly rigid discs, immersed in water and filled with air. The system is driven by an internal acoustic source. The shell has a length L, is clamped along one of its boundaries and is freely supported along the other boundary. Using the infinite domain Green's function, the radiated acoustic pressure is modeled by a hybrid layer potential (linear combination with nonreal coefficient of a simple layer and a double layer). Using Green's tensor of the in vacuo shell operator, the shell displacement is expressed as the sum of the field generated by the acoustic pressures and that due to boundary sources. Finally, the Green's function of the interior Neumann problem is used to express the acoustic pressure inside the shell in terms of the acoustic source and shell normal displacement: this representation fails for any frequency equal to one of the resonance frequencies of the shell interior. To overcome this, a light fluid approximation, which is allowed because the inner fluid is a gas, is adopted. Around each resonance frequency, an inner approximation is defined which matches the classical outer approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular dynamics studies on the local disordering of Σ3 and Σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5°(Σ11), 129.5°(Σ11), 70.5°(Σ3) and 109.5°(Σ3) at various tempratures. The GB structures are found to start local disordering at about 0.5T _m (T _m is the melting point of aluminium) for 50.5°(Σ11), 0.32T _m for 129.5° (Σ11) and 0.38T _m for 70.5°(Σ3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5°(Σ3), this disordering has not been found even when temperature increases up to 0.9T _m . The project supported by the National Natural Science Foundation of China and Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Academia Sinica.     

广义Stokes方程的完全边界积分表示式及其在求解N-S方程中的应用

为了分解N-S方程组各变量相互偶合,本文采用Peaceman-Rachford算子分裂法,将时间相依的N-S方程组分解成不存在上述偶合特性的线性和非线性的子问题。线性子问题具有广义Stokes方程类型。本文采用多重互易法,即采用多阶拉普拉斯算子基本解逐步变换,将其解表示成完全边界积分形式,从而使问题的计算维数降低一维。广义Stokes方程的算例以及二维圆柱在剪切流中的Stokes绕流解,都表明多重互易算法具有高效特点,而且后者与文[3]解析解吻合得非常好。     

软粘土卸载特性计算模型研究

本文从三个方面对软粘土的卸载特性进行了理论研究。采用太沙基一维固结理论，编制了内嵌固结计算的修正剑桥模型程序．对软粘土卸载强度进行了分析。推导了基于修正剑桥模型的孔压表达式并编制了相应的程序对软粘土的卸载孔压特性进行了研究，结果显示，在伸长条件下．孔压先由零逐渐发展到负的最大值．然后又逐渐减小至零。突破零位后，发展成为正孔压并最后达到正的最大值。围压越大，产生的负孔压的极值越大，最终的正孔压越小。将传统边界面模型的线弹性卸载过程改进为弹塑性．建立了软粘土的边界面广义弹塑性模型，从而使边界面模型可用于分析软粘土卸载过程中的塑性变形问题。理论分析结果与试验进行了比较验证，证明理论研究方法是可行的。     

Effect of Free‐Stream Turbulence on the Flow Structure near a Wedge and the Windward Side of an Airfoil

The flow structure behind wire grids is studied for flows with a low subsonic velocity, and the effect of grids on the boundarylayer flow structure is considered. It is shown that the meanvelocity inhomogeneity induced by the grid does not disappear until a distance of 925 calibers downstream of the grid is reached. Liquidcrystal thermography combined with hotwire measurements made it possible to find the source of steady largescale streamwise vortex structures in the boundary layer on a wedge and on an airfoil and to determine the parameters of these structures.     

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.