应用数学和力学

1990 Vol. 11, No. 3

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Numericai-Perturbation Analysis of Edge Effect in Bending Laminated Plate

Ye Bi-quan, Chou Huan-wen

1990, 11(3): 189-194.

Abstract(1505) PDF(479)

Abstract:
In this paper, we consider a bending laminated plate. At first, the dimensionless variables are used to transform the equilibrium equations of any layer to perturbation differential equations. Secondly, the composite expansion is used and the solution domain is divided into interior and boundary layer regions and the mathematical models for the outer solution and the inner solution are yielded respectively. Then, the inner solution is expressed with the boundary intergral equation.

The Improvement of the General Expression for the Stress Function φ of the Two-Dimensional Problem

Zhao Xing-hua

1990, 11(3): 195-202.

Abstract(1676) PDF(502)

Abstract:
In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can't he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.

Material Multipole Mechanics of Elastic Dielectric Composites

Zhou Shu-ang

1990, 11(3): 208-223.

Abstract(1509) PDF(493)

Abstract:
The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

Anisotropy Degree of Nonlinear Solids

Zhang Jin-min

1990, 11(3): 226-232.

Abstract(1654) PDF(430)

Abstract:
This research aims at the generalization of the concept of anisotropy degree of linearly elastic solids which has been defined and investigated in detail by Zhang ^[12] to that of nonlinear and non-elastic solids. The properties of the anisotropy degrees defined here show that they are reasonable.

A Study on Yield and Flow of Orthotropic Materials

Yuan Zu-pei, Zheng Yao

1990, 11(3): 233-238.

Abstract(1778) PDF(588)

Abstract:
On the assumption that the yield criterion of orthotropic materials is isomorphic with Huber-Mises criterion of isotropic materials, we put forward a dimensionless stress yield criterion, and obtained the associated plastic flow law. Using experimental stress-strain curves in various simple stress states, generalized effective stress-strain formulae may be derived correspondingly in various forms.

Some Extended Results of “Subharmonic Resonance Bifurcation Theory of Nonlinear Mathieu Equation”

Chen Yu-shu, Zhan Kai-jun

1990, 11(3): 239-245.

Abstract(1693) PDF(553)

Abstract:
The authors of [1] discussed the subharmonic resonance bifurcation theory of nonlinear Mathieu equation and obtained six bifurcation diagrams in (α,β )-plane. In this paper, we extended the results of[1] and pointed out that there may exist as many as fourteen bifurcation diagrams which are not topologically equivalent to each other.

Several Classes of integrable Nonlinear Ordinary Differential Equations(Ⅰ)——First-Order Equations

Li Hong-xiang, Z. F. Stare

1990, 11(3): 247-252.

Abstract(2027) PDF(1044)

Abstract:
In this paper we give some results of integrability and several classes of integrable equations of first-order nonlinear ordinary differential equations. Many known results of integrability and integrable equations are special cases of them. They may be applied in physics and mechanics, and to derive soliton equations and find soliton solutions.

Uniformly Higher Order Accurate Extrapolations to Solution of Uniformly Convergent Discretization Methods for Singularly Perturbed Problems

Sun Guang-fu

1990, 11(3): 253-258.

Abstract(1691) PDF(500)

Abstract:
We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

Solving the Velocity Parameter of the 2-D Wave Inverse Problems with the Integration-Characteristic Method

Jin Xian-xi

1990, 11(3): 259-266.

Abstract(1650) PDF(426)

Abstract:
For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.

The Singular Perturbation Method Applied to The Nonlinear Stability Problem of A Shallow Spherical Shell (Ⅱ)

Kang Sheng-liang

1990, 11(3): 267-273.

Abstract(1758) PDF(415)

Abstract:
In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11].

Discussion of Critical Load in Nonlinear Stability Analysis and Suggestion of Variational Principle of Solving Critical Loads

Li Long-yuan

1990, 11(3): 275-277.

Abstract(1520) PDF(473)

Abstract:
In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the view point of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.