应用数学和力学

The Problem of Inequality in Solid Mechanics

Guo You-zhong

1989, 10(1): 1-21.

Abstract(1843) PDF(574)

Abstract:
In this paper the problem of inequality in solid mechanics, the contents of which consist of some main concepts, methods and results of the stationary and evolutionary as well as determinate and random problems in variational principle and variational inequality, is studied in detail.

The Evolution Equation of Joint Pdf of Turbulent Velocity and Dissipation

Chen Yi-liang, Pope. S. B.

1989, 10(1): 23-32.

Abstract(2335) PDF(434)

Abstract:
According to the hypothesis that the dissipation of turbulent kinetic energy satisfies log-normal distribution, a stochastic model of dissipation is provided and the Langevin modef^[6] of velocity is modified. Then a joint Pdf equation of turbulent velocity and dissipation is derived. We solve numerically the joint pdf equation using Monte Carlo method and obtain satisfactory results for decaying turbulence and homogeneous turbulent shear flow. The preliminary results show that the model is well working.

The Uniformly Convergent Difference Schemes for a Singular Perturbation Problem of a Self-Adjoint Ordinary Differential Equation

Lin Peng-cheng, Guo Wen

1989, 10(1): 33-41.

Abstract(1537) PDF(423)

Abstract:
In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.

Singular Perturbation of boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on infinite Interval(Ⅰ)

Zhao Wei-li

1989, 10(1): 43-50.

Abstract(1431) PDF(396)

Abstract:
In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameter are examined, where α_i, β are constants, and i=0,1.

Postbuckling of Rectangular Plates under Uniaxlal Compression Combined with Lateral Pressure

Shen Hui-shen

1989, 10(1): 51-58.

Abstract(1543) PDF(491)

Abstract:
Based on the nonlinear large deflection equations of von Kármán plates, the lateral pressure is first converted into an initial deflection by Galerkin method, the postbuckling behavior of simply supported rectangular plates under uniaxial compression combined with lateral pressure is then studied applying perturbation method by taking deflection as perturbation parameter.Two types of in-plane boundary conditions and the effects of initial geometric imperfection are also considered. It is found that the theoretical results are in good accordance with experiments.

On Relations between the Modified-lterative Method and Chien’s Perturbation Solution

Zkou You-he

1989, 10(1): 59-70.

Abstract(1704) PDF(549)

Abstract:
In this paper, we gave analytical formulas of characteristic relation of circular plate in solving high-order solutions of modified-iterative method, which reduces the calculating quantities of the method. Having deduced the relations between the modified-iterative method and Chien's perturbation solution, we obtained the conclusion that the convergent regions of the two methods are the same.

Equation of Axisymmetrical Ring Shells with Variable wall Thickness in Complex Quantity and Its General Solution

Wang Shen-xing

1989, 10(1): 71-78.

Abstract(1506) PDF(398)

Abstract:
The purpose of this paper is to derive the equation of axisymmetrical ring shells with variable wall thickness in complex quantity and to give its general solution.

Lateral Instability of Rectangular Plates

Cheng Xiang-sheng

1989, 10(1): 79-84.

Abstract(1569) PDF(485)

Abstract:
This paper investituites the problems of lateral buckling of rectangular plates. In the text we discuss the minimum critical load of the lateral buckling occurring on under a concentrated force, uniformly distributed load and the concentrated couples, respectively. The energy method is used in this article.

Canonical Representations and Degree of Freedom Formulae of Orthogonal Tensors in n-Dimensional Euclidean Space

Xiong Zhu-hua, Zheng Quan-shui

1989, 10(1): 85-93.

Abstract(2284) PDF(553)

Abstract:
In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part of n/2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

1989 Vol. 10, No. 1