一类非线性方程边值问题的匹配渐近解

利用匹配方法考虑了一类非线性方程边值问题的角层解.首先,由退化问题来决定问题的角层的位置.然后,构造零次近似的外部解和零次近似的内层解,并且对零次近似的外部解和零次近似的内层解进行匹配,由此便得到解的零次近似的形式合成展开式.继而构造一次近似的外部解和一次内层解,并且对一次近似的外部解和一次近似的内层解进行匹配,由此便得到解的一次近似的形式合成展开式.最后利用微分不等式理论证明了得到的一次近似的合成展开式是一致有效的渐近展开式.     

两互相垂直的平面间的层流边界层

本文得到了两互相垂直的平面间的层流边界层的三级近似解.在边界层中,边界层方程中的粘性项和惯性项具有相同的数量级[3].本文则首先假定惯性项大于粘性项去求解边界层方程;然后,令粘性项大于贯性项.最后,取二者的平均值作为边界层方程的真实解.本文所得一级及二级近似解和文献[1]的结果相同.本文的三级近似解则较[1]的结果更精确.     

奇摄动分数阶微分方程的渐近解（英文）

本文研究了一类奇摄动非线性分数阶微分方程初值问题.利用伸长变量构造出解的形式展开式,并利用微分不等式理论,证明了解的一致有效的渐近式.所得的结果具有较好精度的近似解.     

奇摄动分数阶微分方程的渐近解

本文研究了一类奇摄动非线性分数阶微分方程初值问题.利用伸长变量构造出解的形式展开式,并利用微分不等式理论,证明了解的一致有效的渐近式.所得的结果具有较好精度的近似解.     

含参广义向量均衡问题近似解集的连通性

主要研究了含参广义向量均衡问题的几类近似解.在C-次似凸性的条件下,建立了该类含参广义向量均衡问题ε-弱近似解的标量化特征,并得到该类含参广义向量均衡问题两类近似解集的连通性.通过举例说明了所得结果的正确性.     

近似锥一次类凸集值向量优化问题强有效解的广义鞍点刻画

本文研究了近似锥一次类凸集值向量优化强有效解的广义鞍点表示问题.利用择一定理,得到了近似锥-次类凸集值优化问题强有效解为广义鞍点的充分条件和必要条件.所得结果丰富了集值优化理论,并且拓广了广义鞍点的应用.     

含参原始与对偶弱向量近似平衡问题的稳定性

借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.     

含参原始与对偶弱向量近似平衡问题的稳定性北大核心CSCD

借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.     

用双向三角级数法解悬臂矩形薄板在均布荷载下的弯曲

悬臂矩形板的弯曲问题是平板理论中的一个难题.多年来,对于这种板只有能量法与数值解法的近似解.1979年以来清华大学张福范教授等用迭加法陆续得出悬臂矩形板在均布荷载和一些集中荷载作用下的解析解.对于在均布荷载作用下的悬臂矩形薄板,本文用双向三角级数法获得了其挠度函数的解析解,并将所得结果与迭加法所得的结果进行了比较.通过比较表明,两种方法计算的结果符合得十分好,因而相互印证了它们的正确性.     

可渗透壁面上Falkner-Skan磁流体动力学流动的近似解

研究了可渗透壁面上Falkner-Skan磁流体动力学（MHD）边界层流动问题．利用结合了微分变换法（DTM）和Padé近似的DTM-Padé方法,得到了边界层问题的近似解和壁摩擦因数值．通过建立一个迭代程序,边界层问题的近似解被表示为幂级数的形式,而且以图和表形式对不同参数下的近似解结果与打靶法得到的数值结果进行了对比,近似解和数值解结果高度吻合,从而验证了所得问题近似解和结论的可靠性和有效性．并且,对求得的边界层问题近似解结果进行了讨论,分析了不同物理参数对边界层流动的影响．     

受弯层合板边缘效应数值-摄动分析*

本文将分析一个受弯复合材料层合板的计算模型.首先利用无量纲变量将层合板任一层的平衡方程变成以位移表示的摄动型微分方程式;然后利用合成展开法,将求解区域分成内部区域和边界层区域,并推导出求解外部解和内部解的数学模型.为突出边缘效应,最后用边界积分方程表示内部解.     

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.     

On the shear boundary layer of tension plates

The present paper deals with a generic class of problems for plates subjected to loadings combining a high in-plane tension and a small lateral pressure. It develops the governing differential equations in the singular pertubation form, through the postulation of retaining only one of the Kirchhoff's assumptions, that the plate thickness in the boundary layer region is invariant. The solution by using the standard perturbation method is discussed. The postulation is justified when it is demonstrated that in the shear boundary layer the plate thickness is of higher-order smallness. The general method of solution by the standard perturbation technique is applied to an annular plate problem. Problems of different combinations of supports at the inner and the outer boundaries are solved. The case in which both edges are simply supported is presented as an illustration of the solution technique. In other cases results only are presented. The effect of support on the boundaries is also discussed. The shear effect is found to be most significant at a clamped edge. In the special geometry, it is possible to demonstrate that, when the condition on membrane force is not met as required in the general theory, thagnitude of the boundary layer changes. Specifically, the paper presents a case in which the membrhich the membrane force is zero at the inner edge.     

Boundary collocation method for a cracked rectangular plate with double external tension

In this article, the boundary collocation method is employed to investigate the problems of a central crack in a rectangular plate which applied double external tension on the outer boundary under the assumption that the dimensions of the plate are much larger than that of the crack. A set of stress functions has also been proposed based on the theoretical analysis which satisfies the condition that there is no external force on the crack surfaces. It is only necessary to consider the condition on the external boundary. Using boundary collocation method, the linear algebra equations at collocation points are obtained. The least squares method is used to obtain the solution of the equations, so that the unknown coefficients can be obtained. According to the expression of the stress intensity factor at crack tip, we can obtain the numerical results of stress intensity factor. Numerical experiments show that the results coincide with the exact solution of the infinite plate. In particular, this case of the double external tension applied on the outer boundary is seldom studied by boundary collocation method.     

球壳轴对称弯曲问题精确的挠度微分方程及其奇异摄动解

本文提出了球壳轴对称弯曲问题精确的挠度(ω)微分方程和精确的转角(dω/da)微分方程.本文重点研究了挠度微分方程的精度,基本思路是:首先假设边缘效应时经线中面位移u=0,从而建立挠度微分方程,然后再精确地证明挠度微分方程与原来微分方程内力解答完全相同.再精确地证明边缘效应时经线中面位移u=0是精确解.本文给出了挠度微分方程的奇异摄动解,最后验算了平衡条件,证明摄动解求出的内力和外荷载是完全平衡的.这一方面表明摄动解的计算是正确的;另一方面也再二次表明挠度微分方程是精确的微分方程.新微分方程的优点是:1.新微分方程和原来微分方程精度完全相同;2.新微分方程满足的边界条件非常简单;3.新微分方程便于使用摄动解;4.新微分方程可以得到挠度(ω)和转角(dω/da)的表达式.新微分方程使球壳的计算得到很大的简化.本文采用的符号与徐芝纶《弹性力学》第二版下册相同[1].     

Numerical solution of singular perturbation problems by a terminal boundary-value technique

In this paper, we present a new approach for numerically solving linear singularly perturbed two-point boundary-value problems in ordinary differential equations with a boundary layer on the left end of the interval. The original problem is divided into outer and inner region problems. A terminal boundary condition in implicit form is introduced. Then, the outer region problem is solved as a two-point boundary-value problem (TPBVP), and an explicit terminal boundary condition is obtained. In turn, the inner region problem is modified and solved as a TPBVP using the explicit terminal boundary condition. The proposed method is iterative on the terminal point of the inner region. Three numerical examples have been solved to demonstrate the applicability of the method.     

Outer solution for elastic torsion by the method of boundary layer residual states

By the method of boundary layer residual state (BLRS), it is possible to specify the unknown parameters in the general form of the outer asymptotic solution of the governing differential equations for linear boundary value problems (BVP) without any reference to the inner asymptotic solutions of the same problem and the matching procedure. The method accomplishes this task by rationally assigning a portion of the prescribed boundary data to the outer solution. Specifically, the method requires certain weighted averages of the outer solution to be equal to the same averages of the data over the (localized) boundary where the data is prescribed. These weighted averages are consequences of a reciprocity relation inherent in the BVP and the stipulation that the difference between the outer solution and the exact solution (called the residual solution) of the BVP be a boundary layer phenomenon.¶The weighted average requirements are only necessary conditions for the residual state to be a boundary layer. Unfortunately, there are generally countably infinite number of (2) states, many more than the available degrees of freedom in the outer solution to satisfy them. We must show that there is no over-determination or non-uniqueness of the outer asymptotic solution, the abundance of necessary conditions notwithstanding. The present note describes an approach to assuring a well-specified outer solution (up to the expected accuracy) by way of the problem of Saint-Venant torsion. The same approach also also applies to other linear BVP, deducing the appropriate outer solution whenever the determination of the relevant inner solutions is not practical.     

The coupling of bem and fem for the two-dimensional viscous flow problem

In this paper we propose a numerical scheme for treating the problem of sJow viscous flow past an obstacle in the plane. This scheme is a combination of boundary element and finite element methods. By introducing an auxiliary boundary curve, we divide the region under consideration into two subregions, an inner and an outer region. In the inner region, we employ a finite element method (FEM) for solving a system of simplified field equations with proper natural boundary conditions. In the outer region, the solution is expressed in the form of a simple-layer potential with density function satisfying a system of modified integral equations of the first kind. The latter are solved by a boundary element method (BEM). Both solutions are matched on the common auxiliary boundary curve. Error estimates in suitable function spaces are derived in terms of the mesh widths as well as the small parameters, the Reynolds numbers     

用区域分解法求不可压N-S方程的差分解

§1.引言 对不可压小粘性流的数值解,[1]和[2]用奇异摄动观点提出了一个区域分解法.从常微分方程(组)的奇异摄动问题出发,解分解为外部解加边界修正解(以下简称为修正解).外部解的边界条件有:给定(原边界条件)、待定(用原边界条件和修正解)和延拓类.修正解的边界条件有:给定(用原边界条件和外部解延拓)渐近(在边界层外缘)和待定     

各向异性相态场模型的Gibbs—Thompson关系

本文利用奇异摄动的内、外解匹配方法,分析了各向异性时在相态场模型的边界层上表面张菌、法向速度、平均曲率和各向异性函数的影响,得到了各向异性时的Ｇｉｂｂｓ－Ｔｈｏｍｐｓｏｎ关系,以及边界层所满足的方程。