应用数学和力学

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(2018) 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 main conclusion of Poincaré's nonlinear oscillation theory can be extended to continuum mechanics.Besides,in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.

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(1861) 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 mesh sizes are getting too small.Now we propose the boundary layer scheme,which need not take very fine mesh size in the neighbourhood of the boundary layer.Numerical examples show that the accuracy can be satisfied with moderate step size.

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(1751) 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 for different slender ratios and different distances between the body and the plane.It is demonstrated that the proposed method is satisfactory both in convergence and accuracy.Comparison with existing results in the case of prolate spheroid shows that the coincidence is quite good.

Discontinuous and Impulsive Excitation

Liu Zheng-rong

1987, 8(1): 31-36.

Abstract(1973) 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 terms of property of distribution,and by solving x₁(t) and x₂(t) we obtain x(t);finally,we make a thorough investigation about periodic impulsive parametric excitation.

An Analytical Method in the Dynamical Analysis of the Rock Cavity

Yang Sheng-tian

1987, 8(1): 37-42.

Abstract(1629) 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(1948) 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 so-called "general equations"(i.e.have two scalar equations) expressed by the stream function and the theoretical ratio.In this paper we also testify that the equation of evolution for time in plastodynamics problems is neither dissipative nor disperive,and the eigen-equation in plastodynamics problems is a stationary Schrödinger equation,in which we take partial tensor of stress-increment as eigenfunctions and take theoretical ratio as eigenvalues.Thus,We turn nonlinear plastodynamics problems into the solution of linear stationary Schrbdinger equation,and from this we can obtain the general solution of plastodynamics problems with rigid-plastic material.

Equilibrium and Buckling of Combined Shells under Uniform External Pressure

Song Tian-xia, Qin Qing-hua

1987, 8(1): 55-68.

Abstract(1738) 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 be in good agreement with experimental ones.

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(1898) 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 solved numerically.It is found that the effects of free surface on the shape and wave velocity of solitary wave are O(ε²),and the third-order numerical solutions are closer to experimental data than the first-and second-order solutions.

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(1896) 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(in the von Karman sense),are employed separately to analyze the subject.It has been found here that the estimation of the fictitious densities which control the convergence and numerical stability of nonlinear DR solution considering transverse shear effect still needs to be further investigated.In this paper,a procedure to calculate fictitious densities has been presented;hence the numerical stability of this topic has been ensured.In this paper the main steps of solving the nonlinear bending of bimodular composite laminates by means of DR method are outlined.The numerical results are given for simply supported,two-laver cross-ply rectangular plates made of mildly bimodular material(Boron-Epoxy(B-E)) and highly bimodular materials(Aramid-Rubber(A-R) and Polyester-Rubber(P-R)) under sinusoidally distributed and uniformly distributed transverse loads.The resells obtained have been compared with linear results and those;obtained for laminates fabricated from conventional composite materials,the elastic moduli of which are identical with the tensile moduli of the bimodular materials.In addition,the effect of transverse shear deformation on the nondimensionalized center deflection has been studied.

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(1882) 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 to expand the viscous terms,i.e.viscous force,rate of work done by viscous stress and dissipation,in basic aerodynamic equations in the non-orthogonal curvilinear system[2].However,each of these expansions consistes of tens or even hundreds of algebraic terms.The expansions of these three viscous terms discribed in this paper are considerably simplified by analysing their order of magnitude.

1987 Vol. 8, No. 1