Dimensions of attractors for discretizations for Navier-Stokes equations

In this paper, we discretize the 2-D incompressible Navier-Stokes equations with the periodic boundary condition by the finite difference method. We prove that with a shift for discretization, the global solutions exist. After proving some discrete Sobolev inequalities in the sense of finite differences, we prove the existence of the global attractors of the discretized system, and we estimate the upper bounds for the Hausdorff and the fractal dimensions of the attractors. These bounds are indepent of the mesh sizes and are considerably close to those of the continuous version.     

Classical limits for the coefficient of variation for the normal distribution

The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient , the sample size n=1 (1)30,40,60,120, the sample coefficient of variation =0.01(0.01)0.20. It is shown that if n8, 0.20, then the -upper exact classical limits c_u for c are slightly higher than the exact fiducial limits c_u,F for c. if n>8, 0.20, then c_u–c_u,F<5×10^–6.     

杆系结构内力图的程序化作图方法及应用

引入单元局部坐标系和整体坐标系, 根据两种 坐标系中点的对应关系, 推导出整体坐标系中结构内力图上任意一点的坐标公式, 提出了结 构内力图的程序化作图方法. 本文提出的绘图方法可用于杆系结构有限元计算结果的图形显 示.     

系统参数标定以及惯性元件安装误差测量与补偿技术研究

研究了旋转式光纤陀螺捷联惯性导航系统的标定问题。首先分析了系统的安装误差，并建立了陀螺仪、加速度计的输入输出模型，最后给出了相应的标定方法，并给出了具体的实验和数据处理方法。理论分析及实验表明，该方法能够有效地标定出系统的相关参数。     

On physical criteria for the selection of wood for soundboards of musical instruments

In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE, static Young's modulusE, internal frictionQ ^–1 in longitudinal direction, and specific gravity for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ ^–1/(E/), and that there were very high correlations betweenQ ^–1/(E/) andE/, and betweenE andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/, which can be measured easily, and it was derived that the relation betweenE/ andQ ^–1 of wood could be expressed by an exponential equation regardless of wood species.     

Error Bounds for Approximate Solutions for Bending of Unsymmetrically Laminated Plates

Abstract

Certain types of heterogeneous plates exhibit coupling between membrane and flexural effects in their constitutive relations. Such a situation commonly occurs in unsymmetrically laminated plates and in reinforced concrete slabs after cracking. Approximate solutions, principally the “reduced bending stiffness” approximation, have been proposed in the past. The accuracy of this approximation has been examined for several specific cases, but no general investigations have been reported. This paper presents a method for determining bounds on the relative mean square error of approximate solutions to general coupled plate bending problems.     

Sufficient conditions for strong ellipticity for a class of anisotropic materials

We provide sufficient conditions for strong ellipticity for a general class of anisotropic hyperelastic materials. This general class includes as a subclass transversely isotropic materials. Our sufficient conditions require that the first partial derivatives of the reduced-stored energy function satisfy some simple inequalities and that the second partial derivatives satisfy a convexity condition. We also characterize a restricted type of strong ellipticity for a subclass of transversely isotropic materials undergoing pure homogeneous deformations. We apply our results to a model of soft tissue from the biomechanics literature.     

Existence of weak solution for quantum Zakharov equations for plasmas model

Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli theorem, Faedo-Galerkin methods, and compactness property.     

Study of Iterative Algorithms for Solution of Dynamic Contact Problems for Elastic Cracked Bodies

A plane problem is solved for the contact interaction between the faces of a rectilinear crack under the action of a normally incident harmonic tension–compression wave. Iterative algorithms are presented to solve the problem for both given initial distribution of contact forces and given initial discontinuity in the displacements of the crack faces. The convergence rates of the algorithms, the maximum contact forces, and displacement discontinuities are compared.     

Numerical solution of problems for shells of variable stiffness with allowance for transverse shears

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 3, pp. 59–62, March, 1991.     

Numerical-analytic method for the investigation of boundary-value problems for semilinear systems of differential equations

We propose a new numerical-analytic algorithm for the investigation of boundary-value problems for semilinear systems of differential equations.     

Acknowledgement of Reviewers for 2021

Transport in Porous Media -     

空气动力学研讨课建设的探索与实践

为了丰富基础课堂教学资源、满足本科生通识教育的需求,北京航空航天大学近期推出建设名师研讨课、新生研讨课、专业研讨课等,毫无疑问这些对学校本科教学的深化改革具有重要的促进作用.针对我校国家级精品课程空气动力学教学改革的实践,总结了在建设空气动力学名师研讨课过程中的构思和经验,以供参考.空气动力学是一门理论与实际紧密结合的基础课程,在研讨课建设中,提出以空气动力学典型问题为引导,通过启发、实验、讨论、分析等多种形式,引导学生积极主动思考,从鸟的飞行原理、实验现象和结果中获取灵感、凝练科学问题,对激发学习兴趣、提高创新实践能力等具有明显效果.     

Methods for obtaining sufficient conditions for the stability of autonomous conservative systems

A computational method for obtaining sufficient conditions for the stability of the stationary solution of autonomous conservative systems is proposed in the paper. This method is adapted to linear autonomous gyroscopic systems with three degrees of freedom. It is based on the positive definiteness of a parametric quadratic form composed of the gyroscopic force matrices and the potential function. The control parameters for the stability of the zero solution of the gyroscopic system are the entries of the gyroscopic force matrix. The algorithm of the computational method includes estimating one gyroscopic force parameter in the equation constructed from a necessary stability condition.A special example is used to demonstrate the application of this algorithm. Comparison is performed with some well-known methods for obtaining sufficient conditions on the basis of an incomplete set of first integrals of motion. It is shown that the positive definiteness of the modified potential energy may result in stable as well as unstable motions.     

Existence of solutions for periodic boundary value problems for second-order integro-differential equations

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