应用数学和力学

1987 Vol. 8, No. 1

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Extension of Poincare’s Nonlinear Oscillation Theory to Continuum Mechanics(I)-Basic Theory and Method

Huo Lin-chun, Li Li

1987, 8(1): 1-9.

Abstract(2130) PDF(494)

Abstract:
In this paper we extend Poincaré's nonlinear oscillation theory of discrete system to continuum mechanics.First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and non-resonance.By applying the results of linear theory,we prove that...

The Boundary Layer Method for the Solution of Singular Perturbation Problem for the Parabolic Partial Differential Equation

Wu Chi-kuang

1987, 8(1): 11-16.

Abstract(1991) PDF(569)

Abstract:
In this paper,we discuss the singular perturbation problem of the parabolic partial differential equation.As usual,we must reduce the mesh size in the neighbourhood of the boundary layer so that typical feature of the boundary layer will not be lost.Then we need very large operational quantity when ...

The Stokes Flow of an Aribitrary Prolate Axisymmetric Body towards an Infinite Plane Wall

Yuan Fan, Wu Wang-yi

1987, 8(1): 17-30.

Abstract(1865) PDF(472)

Abstract:
By distributing continuously the image Sampsonlets with respect to the plane and.by applying the constant density,the linear and the parabolic approximation,the analytic expressions in closed form for flow field are obtained.The drag factor of the prolate spheroid and the Cassini oval are calculated...

Discontinuous and Impulsive Excitation

Liu Zheng-rong

1987, 8(1): 31-36.

Abstract(2145) PDF(534)

Abstract:
In this paper,we study the solution of differential equation with Dirac function and Heaviside function,arising from discontinuous and impulsive excitation.Firstly,according to the theory of differential equation,we suggest x(t)=x₁(t)+x₂(t)H(t-a);then we derive the equation of x₁(t) and x₂(t) by ter...

An Analytical Method in the Dynamical Analysis of the Rock Cavity

Yang Sheng-tian

1987, 8(1): 37-42.

Abstract(1726) PDF(413)

Abstract:
In this paper,an analytical method in dynamical analysis of the rock cavity is given based on interacted construction of numerical analysis and analytical solution.An example is used to show how to get it in practice.

On the General Equation and the General Solution in Problems for Plastodynamics with Rigid-Plastic Material

Shen Hui-chuan

1987, 8(1): 43-54.

Abstract(2136) PDF(579)

Abstract:
This work is the continuation of the discussion of refs.[1-2].We discuss the dynamics problems of ideal rigid-plastic material in the flow theory of plasticity in this paper.From introduction of the theory of functions of complex variable under Dirac-Pauli representation we can obtain a group of the...

Equilibrium and Buckling of Combined Shells under Uniform External Pressure

Song Tian-xia, Qin Qing-hua

1987, 8(1): 55-68.

Abstract(1859) PDF(472)

Abstract:
Nonlinear strain is used to formulate the energy functional of combined structure with several kind of shells.The nonlinear finite element method(N.F.E.M.) is proposed for calculating bending and buckling of the structure subjected to external hydrostatic pressure.The numerical results are found to ...

Higher-Order Theory of Internal Solitary Waves with a Free Surface in Two-Layer Fluid System of Finite Depth

Zhou Chin-fu

1987, 8(1): 69-77.

Abstract(2072) PDF(503)

Abstract:
A higher-order approximation theory of internal solitary waves with a free surface is presented.Using the method of strained co-ordinates,the third-order approximation evolution equation of interface has been found.An analytic expression of the wave velocity is given.The evolution equation has been ...

Effects of Transverse Shear on the Nonlinear Bending of Rectangular Plates Laminated of Bimodular Composite Materials

Huang Xiao-qing, Dong Wan-lin

1987, 8(1): 79-85.

Abstract(2015) PDF(424)

Abstract:
This paper investigates the application of Dynamic-Relaxation(DR) method to the problems of nonlinear bending of rectangular plates laminated of bimodular composite materials.The classical lamination theory and a shear deformation theory of layered composite plates,taking account of large rotations(...

Simplification of the Expansions of Viscous Terms in Basic Aerodynamic Equations in Non-Orthogonal Curvilinear Coordinate System

Wang Zhong-qi, Kang Shun

1987, 8(1): 87-94.

Abstract(2014) PDF(630)

Abstract:
The application of non-orthogonal curvilinear coordinate system to the calculation of the flow field inside the channel,with complex boundary geometry,can effectively simplify the work of designing the calculation program and improve the accuracy of calculation[1].Therefore,it is obviously necessary...