不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

Studies on structural safety in stochastically excited Duffing oscillator with double potential wells

The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition and Monte–Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio of safe initial points (RSIP) is presented in some given limited domain defined by the system’s Hamiltonian for various parameters or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited by harmonic or stochastic forces, which are different from the customary continuous ones in view of the first-passage problems. In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external harmonic excitation when the Gaussian white noise is also present in the system. The project supported by the National Natural Science Foundation of China (10302025 and 10672140). The English text was polished by Yunming Chen.     

关于结构刚度方程病态问题的疑难分析

本文围绕矩阵位移法求解结构位移的误差，讨论了结构刚度矩阵的病态问题，指出了计算上的病态常常是结构刚度分布和结构拓扑的不合理，而不一定是计算本身的问题。首先，文章依据误差界的概念和范数的性质推导了衡量结构刚度矩阵病态程度的条件数的公式。然后，阐明了基于不同范数的条件数在衡量矩阵病态程度上的等价性。最后，通过两个具有代表性的算例，分别从结构构件的刚度差异和结构几何拓扑两方面，计算和分析了结构刚度矩阵的病态程度随结构本身性质的改变而改变的规律。在特定的算例中，还有使结构刚度矩阵的病态程度降到最低的最佳刚度分布。     

在无单元法里直接准确施加位移边界条件和材料不连续条件

在无单元伽辽金法(EFG)里，由于其滑动最小二乘近似位移函数不满足Kronecker条件，使得它不能准确地施加本质边界条件和材料不连续条件，从而极大地限制了EFG法的发展和进一步应用。本文在位移边界和不同材料交界面的离散结点上采用实际的结点位移值，提出了一种准确施加位移边界和材料不连续条件的方法，该方法实施简单、稳定、求解精度高，而且其推导得出的整体刚度矩阵具有正定、对称和带状分布的特点，可以和有限单元法一样，直接利用各种成熟、高效的线性方程组解法求解系统平衡方程。数值算例结果表明了文中理论和方法的正确性和可靠性。     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

Inertial manifolds for nonautomous infinite dimensional dynamical systems

In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed. Under the spectral gap condition, It is proved that there exist inertial manifolds for a class of nonautonomous evolution equations. Project supported by the National Natural Science Foundation of China     

Assessing and predicting changes in vegetation cover associated with military land use activities using field monitoring data at Fort Hood, Texas

We assessed short-term impacts of changes in military training load on vegetative cover at Fort Hood, TX. From 1989 to 1995, permanent field transects were monitored for vegetative cover and land use disturbance using standard army monitoring methods [Land Condition Trend Analysis (LCTA)]. Land use intensity (training load) was quantified and used to develop a model to predict future vegetation cover values. We found that standard Army monitoring methods detected changes in installation resources associated with changes in training load. Increased training loads were associated with increased measures of disturbance, decreased ground cover, and decreased aerial vegetative cover. We found that the spatial pattern of disturbance and vegetation cover remained relatively constant over the study period despite large variations in overall training load. Our model used the consistency in spatial cover patterns over time and the strong relationship between training load and vegetation cover to predict the impact of future training loads on vegetation.     

Formulation of a Hysteretic Restoring Force Model. Application to Vibration Isolation

This article focuses on the formulation of a hysteretic model used as anisolator restoring force model. The proposed model is based on operatorgoverning input and output functions that depend on the deflection andthe restoring force of the isolator. First, the mathematical formulationis demonstrated, then the hysteretic model proposed is applied toisolators having different types of behavior. The model parameters aresought using the experimental force-deflection loop of each of theisolators studied. Next, the transient response of a flexible structuremounted on an all-metal isolator is predicted by coupling the firstorder differential equation of the restoring force and the second orderdifferential equations of the structure's motion. The experimentalinvestigation validates the proposed hysteretic model applied to theall-metal mount.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ