应用数学和力学

1987 Vol. 8, No. 9

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Nonlinear Analyses for the Postbuckling Behaviors of Annular and Circular Plates

Jiang Fu-ru

1987, 8(9): 755-770.

Abstract(1893) PDF(688)

Abstract:
In this paper we apply the modified method of multiple scales to study the postbuckling behaviors of annular and circular thin plates. The asymptotic solutions have been constructed, the ultimate loads have been determined, and the relations-between the length of twisted waves formed by buckling and the flexural rigidity of plates have been discovered.

On the Circular Footing Plates on Two-Parameters Foundation under Arbitrary Loads

Loo Wen-da, Wang Shu

1987, 8(9): 771-778.

Abstract(1852) PDF(441)

Abstract:
Modelling soils by two-parameter foundation model, this paper calculates the distributions of displacements of circular footing plates on soils and reactions of soils under arbitrary loads using semi-analytical finite element method. And it improves F.Z. Vlazov's solution in the case of axisymmetry. The results agree well in comparison with those by F E M. At the same time, the boundary conditions of circular plates on soils are discussed.

Some Comments on the Original Kaluza-Klein Theory

Amjad Pervez, Asghar Qadir

1987, 8(9): 779-780.

Abstract(3011) PDF(531)

Abstract:
In this note the basis of the Kaluza-Klein theory is examined critically and it is pointed out that the five-dimensional version can't work in the way that was originally intended. The reason why the problem was not noted originally is elucidated.

The Effect of the Hydrodynamic Interaction on the Rheological Properties of Hookean Dumbbell Suspensions in Steady State Shear Flow

Fan Xi-jun

1987, 8(9): 781-789.

Abstract(1868) PDF(473)

Abstract:
The diffusion equation for the configurational distribution function of Hookean dumbbell suspensions with the hydrodynamic interaction(HI) was solved, in terms of Galerkin's method, in steady state shear flow;and viscosity,first and second normal-stress coefficients and molecular stretching were then calculated. The results indicate that the HI included in a microscopic model of molecules gives rise to a significant effect on the macroscopic properties of Hookean dumbbell suspensions. For example, the viscosity and the first normal stress coefficient, decreasing as shear rate increases, are no longer constant;the second normal-stress coefficient, being negative with small absolute value and shear-rate dependent, is no longer zero;and an additional stretching of dumbbells is yielded by the HI. The viscosity function and the first normal-stress coefficient calculated from this method are in agreement with those predicted from the self-consistent average method qualitatively, while the negative second normal-stress coefficient from the former seems to be more reasonable than the positive one from the latter.

Conservation Integrals and Determination of HRR Singularity Fields

Wang Ke-ren, Wang Zi-qiang

1987, 8(9): 791-797.

Abstract(1759) PDF(506)

Abstract:
The angular distribution functions of HRR singularity fields are analyzed via conservation integrals. Two functional equations are proved for the angular distribution-functions andean be used for their solutions. The detailed forms of the functional equations and the final governing equations for solutions are given for the cases of plane strain and plane stress. Accurate numerical results are also given for some typical parameters and the equivalence of different governing equations is proved.

Asymmetrical Growing Delta

Tao Ming-de

1987, 8(9): 799-804.

Abstract(1834) PDF(462)

Abstract:
In this paper, a nonlinear partial differential equation governing a change of shoreline is derived, its solution is expanded as an asymptotic series in a small parameter. Then the Green function is obtained by means of Fourier transform and the solution is expressed using the Green function. The results obtained show that Delta growth is asymmetrical due to sand input from river and longshore current, It tries to explain asymmetrical growth of the Delta of the Changjiang River.

On Discontinuous Period Solution and Discontinuous Solitary Wave of Two-Dimension Shallow Water Equation

Huang Si-xun

1987, 8(9): 805-812.

Abstract(1612) PDF(485)

Abstract:
In this paper we discuss discontiunuous periodic solution and discontinuous solitary wave of the shallow water model of geophysical fluid dynamics. When we consider the properties of trajectory near non-equiubrium point, i.e. singular point, we find that if we introduce the concept of generalized solution(pieccwise smoothing continuous solution), then the system will produce disdontinuous periodic solution and the condition of discontinuous periodic solution can be obtained. When the system is degenerated, we find that the discontinuous solitary wave is existent in the system. In this paper we consider a series of problems and obtain analytic expression of discontinuous solution. This result is compared with squall line in the atmosphere, and both of them are similar.

The Asymptotic Solutions of Axisymmetrical Problems for the Cylindrical Shells with Varying Wall Thickness

Chen Guo-dong

1987, 8(9): 813-824.

Abstract(1785) PDF(543)

Abstract:
In this paper,the uniformly valid asymptotic solutions of axisymmetrical problems for the cylindrical shells with varying wall thickness are given.

Laminar Boundary Layer between Two Planes Perpendicular to Each Other

Yuan Yi-wu

1987, 8(9): 825-831.

Abstract(1698) PDF(499)

Abstract:
In this paper, we obtain a third-order approximate solution for the laminar boundary layer between two planes perpendicular to each other.In boundary layer equations, the viscous and the inertial terms have the same quantity step. In this paper, at first, supposing that the inertial terms are bigger than the viscous terms, we solve the boundary layer equations, and then we suppose that the viscous terms are bigger than the inertial terms. At last, we take the mean value as the valid solution of the boundary layer equations.The first-and the second-order approximate solutions obtained in this paper coincide with the results in ref. [1], while the third-order solution obtained in this paper is better than that in ref. [1].

Chaotic Behavior of the Measure-Preserving Mappings with Odd Dimension

Cheng Bao-long

1987, 8(9): 833-838.

Abstract(1764) PDF(558)

Abstract:
In this paper, we consider the measure-preserving mapping C with dimension 3 which is also the expansion of Henon mapping. Then we study the character of its fixed points and chaotic behavior. Next we offer a possibility that using the chaotic behavior of the lower dimensional mappings brings about the higher.

Analysis of the Motion of a Gyro-theodolite

Wang Hong-lan

1987, 8(9): 839-848.

Abstract(1929) PDF(727)

Abstract:
With the method of analytical mechanics, this paper studies the motions of a gyro-theodolite under the action of(1) the torque of gravity only,(2) the torque applied by the band suspension,(3) the torque of the band suspension with air damping considered, the equations of motion are then established and their solutions are found. Furthermore, analysis of the law of Motion and the behaviour of gyro-theodolite during the orientation is made.