2000 Vol. 21, No. 3

Display Method:
2000, 21(3): 221-225.
Abstract(2011) PDF(739)
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.
2000, 21(3): 226-234.
Abstract(2363) PDF(821)
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.
2000, 21(3): 235-244.
Abstract(2314) PDF(506)
Abstract:
Bifurcations of one kind of reaction-diffusion equations, u″+μ(u-uk)=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.
2000, 21(3): 245-252.
Abstract(1791) PDF(602)
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.
2000, 21(3): 253-259.
Abstract(1828) PDF(727)
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∈RN>(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (uλ,vλ). Moreover:uλ and vλ are strictly increasing with respect to λ.
2000, 21(3): 260-264.
Abstract(1533) PDF(585)
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.
2000, 21(3): 265-276.
Abstract(2012) PDF(1168)
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.
2000, 21(3): 277-284.
Abstract(1953) PDF(555)
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.
2000, 21(3): 285-289.
Abstract(1964) PDF(595)
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.
2000, 21(3): 290-296.
Abstract(2147) PDF(656)
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.
2000, 21(3): 297-300.
Abstract(2253) PDF(705)
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.
2000, 21(3): 301-306.
Abstract(1918) PDF(477)
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.
2000, 21(3): 307-314.
Abstract(1652) PDF(440)
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.
2000, 21(3): 315-322.
Abstract(1822) PDF(758)
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.
2000, 21(3): 323-330.
Abstract(2086) PDF(678)
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.