应用数学和力学

2000 Vol. 21, No. 3

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Equations of Motion and Boundary Conditions of Incremental Rate Type for Polar Continua

Dai Tianmin

2000, 21(3): 221-225.

Abstract(2175) PDF(742)

Abstract:
The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff form for polar continua are obtained in combination of theser esults with those for classical continuum mechanics derived by Kuang Zhen.

Bifurcation Analysis of a Double Pendulum With Internal Resonance

Bi Qinsheng, Chen Yushu

2000, 21(3): 226-234.

Abstract(2457) PDF(827)

Abstract:
By employing the normal form theory, the Hopf bifurcation and the transition boundary of an autonomous double pendulum with 1:1 internal resonance at the critical point is studied. The results are compared with numerical solutions. Further, by numerical methods, the road to chaos of a non-autonomous system is presented in the end.

A Note on Bifurcations of u″+μ(u-u^k)=0(4≤k∈Z⁺)

Li Changpin

2000, 21(3): 235-244.

Abstract(2469) PDF(509)

Abstract:
Bifurcations of one kind of reaction-diffusion equations, u″+μ(u-u^k)=0(μ is a parameter,4≤k∈Z⁺),with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov-Schmidt reduction, satisfactory results can be acquired.

A Theoretical Research to Effective Viscosity of Colloidal Dispersions

Gu Guoqing, Yu Kinwah

2000, 21(3): 245-252.

Abstract(1892) PDF(606)

Abstract:
Colloidal dispersions are common in nature with wide industrial applications. One of the central theoretical problems in the field is to determine the rheological properties of the colloidal dispersion from the microstructures of the systems. Because of the difficulties associated with the boundary-value problems of the many-particle system, existing theories for colloidal suspensions are limited to low particle concentrations. In this work, we develop a method of transformation field is developed by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops). The predictions of our theory are in good agreement with the Einstein's formula for suspensions and the Taylor's formula for emulsions at low particle concentrations. At higher particle concentrations, the results of Nunan and Keller are produced. The method is also applicable to the viscosity of colloidal systems with non-spherical particles.

Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term

Nicolae Tarfulea

2000, 21(3): 253-259.

Abstract(1976) PDF(730)

Abstract:
It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system:-$u=λu|u|^q-1+u|u|^p-1-vinΩ, -$v=δu-γvin Ω,u=v=0 onΩ,where Ω∈R^N>(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (u_λ,v_λ). Moreover:u_λ and v_λ are strictly increasing with respect to λ.

The Existence of Periodic Solutions of Impulsive Differential Equations of Mixed Type

Fang Hui

2000, 21(3): 260-264.

Abstract(1676) PDF(588)

Abstract:
The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.

On Equation of Discrete Solid Particles’ Motion in Arbitrary Flow Field and Its Properties

Huang Shehua, Li Wei, Cheng Liangjun

2000, 21(3): 265-276.

Abstract(2141) PDF(1171)

Abstract:
The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.

Probability of Random Events of Inspection and Repair and Maintaining Reliability of Structures

Guo Shuxiang, LÜ Zhenzhou

2000, 21(3): 277-284.

Abstract(2045) PDF(558)

Abstract:
Reliability analysis of the inspected and repaired structure requires dealing with a large number of complex random events. Considering many kinds of random factors, a probability of these random events existing possibly in the inspection and repair process and reliabiity analysis methodologies are proposed. A systematic dynamic reliability model is given for structures in service under the scheduled inspection and repair.

Long-Time Behavior of Transient Solutions for Cellular Neural Network Systems

Jiang Yaolin

2000, 21(3): 285-289.

Abstract(2169) PDF(598)

Abstract:
By establishing concept on transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.

Generalized Variational Principle on Nonlinear Theory of Naturally Curved and Twisted Closed Thin-Walled Composite Beams

Yu Aimin

2000, 21(3): 290-296.

Abstract(2293) PDF(659)

Abstract:
Naturally curved and twisted closed thin-walled slender beams of composite material undergoing small strains, large displacements and rotations have been investigated, and an incomplete generalized variational function on theory of elasticity with finite displacement is established for these beams with complete constrained boundaries at two ends. The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition. The above-mentioned method can also be extended to other various incomplete constrained boundaries conveniently. In addition, the fundamental equations and concerned formulas in the small displacement theory of the beams can be derived by using above results.

Uniqueness for the Solutions of Elastic Thin Plates and Shallow Shells as Well as Their Contact Problem With Half Space

Fan Jiashen

2000, 21(3): 297-300.

Abstract(2398) PDF(709)

Abstract:
The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

F.E.M. Analysis of Delamination Buckling in Composite Plates & Shells

Zhu Jufen, Zheng Gang, Wu Jinying

2000, 21(3): 301-306.

Abstract(2110) PDF(482)

Abstract:
The purpose of the present study is to develop a new finite element method for analyzing buckling of delaminated composite plates and shells. This is achieved by establishing a new finite element called the reference-surface element. By use of the compatibility condition under Mindlin assumptions, the formulation of the reference-surface element was derived from whichever plate-element or shell-element being capable of analyzing composite plates and shells. This method assures a reasonable description of displacement field and the satisfaction of compatibility conditions for delamination problem. Numerical results for linear delamination buckling of axially compressed shells are presented to validate the method.

Mathematical Theory of k Multiplier

Yang Wenxiong

2000, 21(3): 307-314.

Abstract(1792) PDF(444)

Abstract:
On the power unit vector presented by Yang Wenxiong, it for the mathematical theory of k multiplier is extended to create a new mathematical branch. The extended k multiplier is yet to concern the negative powers. Enumerating the combinatorial variaties and its functions can satisfy the various conditions, formulas, integrations, and equations etc. derived by Yang Wenxiong. The theory of k multiplier will be applied further to establish the theory of supperlight of a particle and its motion with the natural wave-particle duality etc.

Existence of Solutions for Periodic Boundary Value Problem for Second Order Integro-Differential Equations

Hong Shihuang, Hu Shigeng

2000, 21(3): 315-322.

Abstract(1934) PDF(761)

Abstract:
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second order nonlinear integro-differential equations in Banach Spaces is proved.

Periodic Boundary Value Problems for First Order Integrodifferential Equations of Mixed Type

Zhang Fubao

2000, 21(3): 323-330.

Abstract(2269) PDF(682)

Abstract:
The existence of at least one solution and the existence of extreme solutions of periodic boundary value problems for first order integrodifferential equations of mixed type are studied,in the presence of generalized upper and lower solutions. The discussion is based on new comparative theorems and coincidence degree and monotone iterative methods.