应用数学和力学

1991 Vol. 12, No. 2

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Theory of Nonlinear Dynamic Stability for Composite Laminated Plates

Zhou Cheng-ti

1991, 12(2): 101-108.

Abstract(2216) PDF(676)

Abstract:
In this paper, the general equations of dynamic stability for composite laminated plates are derived hyHamilton principle. These general equations can he used to consider those different factors that affect the dynamic stability of laminated plates. The factors are transverse shear deformation, initial imperfections, longitudinal and rotational inertia, and ply-angle of the fiber, etc. The solutions of the fundamental equations show that some important characteristics of the dynamic instability can only be got by the consideration and analysis of those factors.

On the Boundary Value Problems for Ordinary Differential Equations with Turning Points

Jiang Fu-ru

1991, 12(2): 108-117.

Abstract(2094) PDF(624)

Abstract:
In this paper, we consider the boundary value problems of the form ey"-f(x,e)y'+g(x,e)y=0(-a≤x≤b,0<ε≤1)y(-a)=a,y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.

Analytical Solutions of Singularities Moving with an Arbitrary Path when Two Fluids Are Present

He You-sheng, Lu Chuan-jing, Chen Xue-nong

1991, 12(2): 119-134.

Abstract(2288) PDF(550)

Abstract:
The derivations are carried out for the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present. In such a case, the pressure distribution is no longer equal to a constant or zero at the free interface. Taking the influence of an upper fluid upon the lower fluid into consideration, a series of fundamental solutions in closed forms arc presented in this paper.

Constructions of the General Solution for a System of Partial Differential Equations with Variable Coefficients

Zhang Hong-qing, Yang Guang

1991, 12(2): 135-139.

Abstract(2853) PDF(831)

Abstract:
Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.

Equilibrium Problems of Spherically Isotropic Bodies

Ding Hao-jiang, Ren Yong-jian

1991, 12(2): 141-148.

Abstract(2063) PDF(646)

Abstract:
In this paper the displacements and body-forces are resolved, respectively, and the 3-dimensional equilibrium problems of spherically isotropic bodies with body-forces are transferred into a two-order differential equation and a four-order differential equation. Based on the series expansion technique and properties of spherical functions, the series solutions are obtained for the corresponding homogeneous equations, which can be adapted to solve equilibrium problems oj whole spheres or spherical shells. The special solution for a revolving sphere is also given.

The Displacement Solution of Conical Shell and Its Application

Huang Yi

1991, 12(2): 149-164.

Abstract(2022) PDF(609)

Abstract:
In this paper, the displacement solution method of the conical shell is presented. From the 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. As special cases of this paper, the displacement function introduced by V. Z. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell and that of the circular plate are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell is reduced to finding the displacement function U(s,θ),and the general solution of the governing equation is obtained in generalized hypergeometric function, For the axisymmetric bending deformation of the conical shell, the general solution is expressed in the Bessel functionOn the basis of the governing equation obtained in this paper, the differential equation of conical shell on the elastic foundation(A Winkler Medium) is deduced, its general solutions are given in a power series, and the numerical calculations are carried out.

The Exact Integral Equation of Hertz’s Contact Problem

Yun Tian-quan

1991, 12(2): 165-169.

Abstract(2351) PDF(513)

Abstract:
This paper presents the exact integral equation of Hertz's contact problem, which is obtained by taking into account the horizontal displacement of points in the contacted surfaces due to pressure.

Turbulent Coherent Structure and Dynamic System

Li Jia-chun

1991, 12(2): 171-176.

Abstract(2108) PDF(589)

Abstract:
The main difficulties in the study of turbulence via dynamic system lie in how to relate continuum systems of infinite dimension with dynamic system in low dimension space and how to depict its spacial structure. In this paper, we'll give a comprehensive review on various methods to describe complex systems in low dimension space and new approaches to the resolution of turbulence problems.

Crack Problem for an Inhomogeneous Plane Bonded by Two Different Inhomogeneous Half-Planes

Tang Ren-ji

1991, 12(2): 177-183.

Abstract(1903) PDF(509)

Abstract:
In this paper the crack problem for two bonded inhomogeneous half-planes is considered. It is assumed that the different materials have the same Poisson ratio v, but generally speaking, both Young's moduli vary exponentially with the coordinate x in different form. Using the single crack solution of the inhomogeneous plane problem and Fourier transform technique, the problem is reduced to a Cauchy-type singular integral equation. Several numerical examples to calculate the stress intensity factors are carried out.

The Global Bifurcation Structure of a Kind of Digit Mapping

Lu Qin-he, Xu Zheng-fan, Lin Fu-qin, Liu Zeng-rong

1991, 12(2): 185-193.

Abstract(1862) PDF(628)

Abstract:
The global structure of the mapping T_n:x→[x²]_n is studied. The symmetric unconnected substructures of T₂ is coincident with [1] by computer, but for n=3 the symmetry of these substructures vanishes. As n is increasing, the global bifurcation structure of T₂ is shown. Finally, similar results for the mapping T_n:x→[μx²]_n are also proved.

The Effect of Transverse Shear Deformation on Stress Concentration Factors for Shallow Shells with a Small Circular Hole

Loo Wen-da, Cheng Yao-shun

1991, 12(2): 195-202.

Abstract(1916) PDF(605)

Abstract:
Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole. General solutions of the equations are obtained, in terms of series, for shallow spherical shells and shallow circular cylindrical shells with a small circular hole. Approximate explicit solutions and numerical results are obtianed for the stress concentration factors of shallow circular cylindrical shells with a small hole on which uniform pressure is acting.