SOLUTION OF A RESEARCH PROBLEM

ＳＯＬＵＴＩＯＮＯＦＡＲＥＳＥＡＲＣＨＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（巫世权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇｓｈａ４１００７３，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

SOME GREEDY t-INTERSECTING FAMILIES OF FINITE SEQUENCES

ＳＯＭＥＧＲＥＥＤＹｔ－ＩＮＴＥＲＳＥＣＴＩＮＧＦＡＭＩＬＩＥＳＯＦＦＩＮＩＴＥＳＥＱＵＥＮＣＥＳ￥ＷＵＳＨＩＱＵＡＮ（巫世权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇ...     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

A NICE PROPERTY OF OPERATORS DEFINED ON c_o

ＡＮＩＣＥＰＲＯＰＥＲＴＹＯＦＯＰＥＲＡＴＯＲＳＤＥＦＩＮＥＤＯＮｃ＿ｏＣ．Ｓｗａｒｔｚ（ＮｅｗＭｅｘｉｃｏＳｔａｔｅＵｎｉｖｒｓｉｔｙ，ＬａｓＣｒｕｃｅｓ，Ｕ．Ｓ．Ａ．）Ｍｉｎ－ＨｙｕｎｇＣｈｏ（Ｋｕｍ－ＯｈＵｎｉｖｅｒｓｔｙｏｆＴｅｃｈｎｏｌｏｇ...     

ESTIMATES OF EIGENVALUES FOR UNIFORMLY ELLIPTIC OPERATOR OF SECOND ORDER

ＥＳＴＩＭＡＴＥＳＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＵＮＩＦＯＲＭＬＹＥＬＬＩＰＴＩＣＯＰＥＲＡＴＯＲＯＦＳＥＣＯＮＤＯＲＤＥＲＱＩＡＮＣＨＵＮＬＩＮ（钱椿林）ＣＨＥＮＺＵＣＨＩ（陈祖墀）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｔｎａｔｉｃｓ，Ｕｎｉｖｅｒ...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

A CLASS OF SINGULARLY PERTURBED NONLINEAR ROBIN PROBLEMS

ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＬＹＰＥＲＴＵＲＢＥＤＮＯＮＬＩＮＥＡＲＲＯＢＩＮＰＲＯＢＬＥＭＳＺｈａｏＷｅｉｌｉ（赵为礼）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ１３００２３，Ｃｈｉｎａ...     

REPRESENTATIONS AND ENUMERATIONS OF SEMIORDERS WITH HEIGHT ONE

ＲＥＰＲＥＳＥＮＴＡＴＩＯＮＳＡＮＤＥＮＵＭＥＲＡＴＩＯＮＳＯＦＳＥＭＩＯＲＤＥＲＳＷＩＴＨＨＥＩＧＨＴＯＮＥＷｕＳｈｉｑｕａｎ（巫世权）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓＰ...     

THE PERIODIC SOLUTIONS OF A CLASS OF CUBIC DELAY DIFFERENTIAL SYSTEM

ＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＣＵＢＩＣＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＣＨＥＮＹＯＮＧＳＨＡＯ（陈永劭）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｎｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔ...     

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＩＮＤＥＣＯＭＰＯＳＡＢＬＥＤＥＦＩＮＩＴＥＨＥＲＭＩＴＩＡＮＦＯＲＭＳ￥ＺＨＵＦＵＺＵ（ＤｅｐａｒｔｍｅｌｌｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙｔＳｈａｎｇｈａｉ２０００６２，...     

A novel matrix method for coupled vibration and damping effect analyses of liquid-filled circular cylindrical shells with partially constrained layer damping under harmonic excitation

A novel matrix method is further developed for a liquid-filled circular cylindrical shell with partially constrained layer damping (CLD), which consists of treating liquid domain with Bessel function approach, and shell domain with transfer matrix equation based on a new set of first order matrix differential equation. In order to indicate its advantage to the finite element method (FEM), free vibration analysis on such an empty shell under clamped–clamped boundary are carried out by using the present method together with FEM. Meanwhile, coincident result is yielded for the liquid-filled shell by adopting the present method with by other transfer matrix method. Finally, a series of valuable numerical results are obtained by this method.     

A finite volume element method for simulating secondary settling tanks

This contribution summarizes a new finite volume element (FVE) method as a unified scheme for coupled sedimentation-flow problems in secondary settling tanks in wastewater treatment. The model is two-dimensional in an axisymmetric setting. A new numerical example is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

夹层圆板的大幅度振动

本文利用哈密顿原理导出了夹层圆板轴对称大幅度自由振动的基本方程,并给出了表板很薄情况下的简化形式.作为算例,利用修正迭代法求出了具有滑动固定边界条件夹层圆板对轴称大幅度自由振动的一种解析解,并由此导出了夹层圆板振幅和振频的解析关系式.     

密封容器组合壳自由振动的精确解

给出了一类密封容器组合壳自由振动问题的精确解,基于Love经典薄壳理论,导出了具有任意经线形状的旋转壳体在轴对称振动时的基本方程,组合壳结构中球壳与柱壳的连接条件是通过连接处的变形连续性和内力平衡关系得出的。问题的数学模型被归结为常微分方程组在球壳和 壳两个区间上的特征值问题。振动模态函数是由Legendre和三角函数构造出来,并且得到了精确的频率方程。所有的计算都是在Maple程序下运行的,无论是精确的符号运算还是具有所需有效数学精度的数值计算,都表明该文所编译的Maple程序是简单而有效的。固有频率的数值结果同文献中有限元法和其它数值方法的结果作了比较。作为一个标准,该文给出的精确解对于检验各种近似方法的精密度是有价值的。     

Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain–displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.     

The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations

We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknowns. This is contrary to suggestions in the existing literature that line relaxations and semicoarsening are needed in multigrid algorithms to overcome difficulties caused by the singularities in the axisymmetric Maxwell problems. Our multigrid analysis proceeds by applying the well known regularity based multigrid theory. In order to apply this theory, we prove regularity results for the axisymmetric Laplace and Maxwell equations in certain weighted Sobolev spaces. These, together with some new finite element error estimates in certain weighted Sobolev norms, are the main ingredients of our analysis.

     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.     

Static and dynamic analysis of two-layer Timoshenko composite beams by weak-form quadrature element method

To improve the efficiency in predicting the dynamic mode and static response of the two-layer partial interaction composite beams, this paper utilizes the differential quadrature technique to approximate derivatives of the primary unknowns with adaptive order of precision, rather than the low and constant order of interpolation used in the conventional finite element method (FEM). A degree-of-freedom-adaptive weak-form quadrature element (WQE) for dynamic analysis is formulated and implemented based on the principle of virtual work. For the purpose of comparison, a parabolic displacement-based finite element is also provided, thus (1) the predicted deflections and natural frequencies of the composite beams are verified; (2) the smoothness of the internal forces and stresses generated by WQE method and FEM are compared, and (3) the convergent rates of higher order free vibration modes are also examined. Numerical results show that the efficiency of the proposed WQE method has, on the one hand, significantly triumphed over that of FEM on analyses including static response, natural frequencies and higher order free vibration modes, on the other hand, the smoothness of results, including internal forces and stresses, is greatly refined.     

Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip procedures

This research describes spectral finite element formulation for vibration analysis of rectangular symmetric cross-ply laminated composite plates of Levy-type based on classical lamination plate theory (CLPT). Formulation based on SFEM includes partial differential equations of motion, spectral displacement field, dynamic shape functions, and spectral element stiffness matrix (SESM). In this paper, vibration analysis of composite plate is investigated in two sections: free vibrations and forced vibrations. In free vibrations, natural frequencies are calculated for different Young’s moduli ratios and boundary conditions. In forced vibrations, plate vibrations are investigated under high-frequency concentrated impulsive loads. The resulting responses due to spectral element formulation are compared with those of (time-domain) finite element and analytical formulations, whenever available. The results demonstrate the superiority of SFEM with respect to FEM, in reducing computational burden, simultaneously increasing numerical accuracy, specifically for excitations of high-frequency content. By reducing the time duration of impulsive loads, and consequently increasing the modal contribution of higher modes in the transient response of plate, the accuracy of FEM responses decreases substantially accompanied with a high volume of computations, while the accuracy of the SFEM response results is very high and simultaneously, with a low computational burden. Practically, SFEM follows very closely exact analytical solutions.