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1.
In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs. [3,4]. 相似文献
2.
Li Wen-shen 《应用数学和力学(英文版)》1994,15(5):491-498
The generalized KdV equationu
1+auua+μua3+eua5=0[1] is a typical integrable equation. It is derived studying the dissemination of magnet sound wave in cold plasma[2], the isolated wave in transmission line[3], and the isolated wave in the boundary surface of the divided layer fluid[4]. For the characteristic problem of the generalized KdV equation, this paper, based on the Riemann function, designs a suitable
structure, then changes the characteristic problem to an equivalent integral and differential equation whose corresponding
fixed point, the above integral differential equation has a unique regular solution, so the characteristic problem of the
generalized KdV equation has a unique solution. The iteration solution derived from the integral differential equation sequence
is uniformly convegent in
. 相似文献
3.
The problem of the beginning of motion of a cut in a plane under symmetric external loading is considered. The material lying
on the cut continuation forms a layer (interaction layer). A transition to a plastic state within the layer is assumed to
be possible. The behavior of the layer is described by an ideally elastoplastic model, and the plane outside the layer is
assumed to be linearly elastic. A system of boundary integral equations for determining the stress-strain state is derived.
Based on this system, a discrete model of separation of the layer material is constructed under the assumption of a constant
stress-strain state in the element of the interaction layer. The distribution of stresses in the pre-fracture zone is determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 187–195, July–August, 2009 相似文献
4.
Based on the Kantorovich approximation solution for a rectangular plate in bending, this paper deals with the solutions for the ladder plate with various boundary conditions. The deflection of the plate is expressed in a first-order displacement function w(x,y)=u(x,y)v(y) where the u(x,y) in x direction is the generalized beam function. By making use of the principle of least potential energy, the variable coefficients differential equations for v(y) may be established. By solving is, these differential eugations and making use of the boundary conditions, the accurate solutions of v(y) in y direction may be obtained. Then the displacement function w(x,y) is the solution for the problem of the bending of the ladder plate with a better degree of approximation. 相似文献
5.
By using the method in[3],several useful estimations of the derivatives of the solutionof the boundary value problem for a nonlinear ordinary differential equation with a turningpoint are obtained.With the help of the technique in[4],the uniform convergence on thesmall parameterεfor a difference scheme is proved.At the end of this paper,a numericalexample is given.The numerical result coincides with theoretical analysis. 相似文献
6.
非线性转子-轴承系统的周期解及近似解析表达式 总被引:2,自引:0,他引:2
通过对普通打靶方法进行改造提出一种确定非线性系统周期轨道及周期的新型打靶算法。首先通过改变系统的时间尺度,将非线性系统周期轨道的周期显式地出现在非线性系统的系统方程中,然后对传统打靶法进行改造,将周期也作为一个参数一起参与打靶法的迭代过程,迭代过程包含对周期轨道和周期的求解,迭代过程中的增量通过优化方法选择,从而能迅速确定出系统的周期轨道及其周期。应用所求的结果结合谐波平衡方法求得了非线性系统的周期轨道的近似解析表达式,理论上通过增加谐波的阶数任何精度的周期解都可以得到。最后将该方法应用于非线性转子轴承系统,求出了在某些参数下转子的周期解及其近似解析表达式,通过与四阶Runge-Kutta数值积分结果比较,验证了方法的有效性,计算结果对于转子系统运动的定量控制有重要理论指导意义。 相似文献
7.
GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE
IntroductionItiswell_knownthatpseudo_parabolicequationwithprincipalpartut -uxxthasbeenstudyingrecently ,becausethereexistswidephysicalbackgroundforthisclassofequations.[1 ]studiedthemulti_dimensioninverseproblemforthefollowingclassofnonlinearevolutionequ… 相似文献
8.
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) 相似文献
9.
IntroductionIn recent years,the theory of variational inclusion has appeared as an elegant andfascinating branch of pure and applied mathematics.This theory provides us with a convenientmathematical apparatus for uniformly studying a wide range of problem… 相似文献
10.
A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means
of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in
detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results
of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow
past cones with various apex-angles at different cavitation numbers. The numerical results are found in good agreement with
experimental data.
The project supported by the National Natural Science Foundation of China 相似文献
11.
Yun Tianquan 《应用数学和力学(英文版)》1999,20(1):36-42
The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outsidergeion-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality. Examples of part ofthese singular sources such as Kelvin’s point force, Point-Ring-Couple (PRC) etc.are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application. 相似文献
12.
二维边界层方程的迭代求解 总被引:2,自引:1,他引:1
针对二维边界层方程,提出了分析积分迭代法.首先将该方法应用于Blasius方程和Falkner-Skan方程的求解,数值计算结果稳定,计算精度高;然后对外部有势流不能达到自相似要求、必须二维求解的二维层流边界层问题,在分析积分迭代法中加上计算力学的松弛迭代法,形成了一套有效的算法.数值结果表明该方法用于层流边界层的计算是很有效的. 相似文献
13.
The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem. 相似文献
14.
Yizhou Chen 《力学快报》2011,1(3):031005
This paper studies a numerical solution of multiple hole problem by using a boundary integral equation. The studied problem can be considered as a supposition of many single hole problems. After considering the interaction among holes, an algebraic equation is formulated, which is then solved by using an iteration technique. The hoop stress around holes can be finally determined. One numerical example is provided to check its accuracy. 相似文献
15.
罗元松 《应用数学和力学(英文版)》2001,22(4):478-482
IntroductionandPreliminariesThroughoutthispaper,weassumethatHisarealHilbertspace ,〈· ,·〉istheinnerproductonH ,PisaconeinH .ByvirtueofthecomeP ,anorder“≤”isinducedinH ,i.e .,foranygivenx,y∈H ,x≤yifandonlyify -x∈P .Amulti_valuedmappingA :D(A) H → 2 Hissaidtobeaccretiv… 相似文献
16.
袁镒吾 《应用数学和力学(英文版)》1988,9(8):777-786
In this paper, we study the approximate solution of the self-simikar problem for radial flow of non-Newtonian fluids through
porous media. Assuming that the fluids obey the exponential function law, we obtain an exact solution for the exponent n=0
and compare it with the approximate solution in ref. [1].
For n>1 and n<1, we obtain respectively approximate solutions. Some exampls are presented. 相似文献
17.
18.
莫嘉琪 《应用数学和力学(英文版)》2010,31(12):1577-1584
A generalized nonlinear disturbed Klein-Gordon equation is studied. Using the homotopic mapping method, the corresponding homotopic mapping is constructed. A suitable initial approximation is selected, and an arbitrary-order approximate solution to the soliton is calculated: A weakly disturbed equation is also studied. 相似文献
19.
李清溪 《应用数学和力学(英文版)》1987,8(5):419-425
The convergence of approximate solutions of boundary value problem of fourth order elliptic differential equations with uncontinuous coefficients in a rectangular region is investigated in this paper. This is useful for certain bending problems of rectangular plate on elastic supports. 相似文献