应用数学和力学

1987 Vol. 8, No. 5

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Tang Xie-li, Yeh Kai-yuan

1987, 8(5): 385-392.

Abstract(1808) PDF(544)

Abstract:
According to the principle of minimum complementary energy a mathematical statement of optimal strength design problem for elastic beams is formulated in this research, which is an extremum problem of functionals with equality and inequality constraints. Further the application of the Lagrangian multiplier method yields the necessary conditions for extrema. A set of relations that must be satisfied for the optimal solution follows afterwards. This set of relations can be used to verify the optimality of a uniform strength design or any feasible elastic design. An iterative numerical method to find the optimal solution when the uniform strength design is not optimal is also presented in this paper.

A Note on the Method of Weighted Difference

Wu Chi-kuang

1987, 8(5): 393-397.

Abstract(2193) PDF(484)

Abstract:
In this short paper, we introduce a new difference approximation for singular perturbation problem and prove the necessary condition of uniform convergence. Selecting apposite weight factor, we obtain the same difference schemes as in the case of Ilin's method.

Incremental Virtual Work Equation for Geometric Nonlinear Analysis

Wang Ying-jian

1987, 8(5): 399-404.

Abstract(1867) PDF(506)

Abstract:
In this paper, an incremental virtual work equation is derived. It is suitable for geometric nonlinear analysis in finite element method. The effect of truncation errors is considered in the incremental virtual work equation.

Convergence of the Approximate Solution for the Elliptic Boundary Value Problem

Li Qing-xi

1987, 8(5): 405-411.

Abstract(1589) PDF(490)

Abstract:
The convergence of approximate solutions of boundary value problem of fourth order elliptic differential equations with uncontinuous coefficients in a rectangular region is investigated in this paper. This is useful for certain bending problems of rectangular plate on elastic supports.

Some Phenomena for Weak Spring Duffing Equation in Subharmonic and Ultrasubharmonic Region

Xu Zhen-yuan, Liu Zeng-rong

1987, 8(5): 413-418.

Abstract(1688) PDF(606)

Abstract:
In this paper the situation in which weak spring Duffing equation gets into the chaos on account of small perturbation is discussed with Melnikov-Holmes' method, and some phenomena in which the different subharmonic and the ultrasubharmonic coexist with the chaos are discovered.

Exact Solution of the Boltzmann Equation

Shen Hui-chuan

1987, 8(5): 419-431.

Abstract(2377) PDF(667)

Abstract:
We build up immediate connection between the nonlinear Boltzmann transport equation and the linear AKNS equation, and classify the Boltzmann equation as the Dirac equation by a new method for solving the Boltzmann equation out of keeping with the Chapman, Enskog and Grad's way in this paper. Without the effect of other external fields, the exact solution of the Boltzmann equation can be obtained by the inverse scattering method.

On The Jumping Problems of A Circular Thin Plate With Initial Deflection

Qin Sheng-li, Zhang Ai-shu

1987, 8(5): 433-443.

Abstract(1747) PDF(479)

Abstract:
In this paper, the jumping problems of a circular thin plate with initial deflection are studied by using the method of two variables,^[3][4]proposed by Jiang Fu-ru and the method of the normal perturbation (in this paper (1.1), (1.2)). We obtain Nth-order uniformly valid asymptotic expansion of the solution of this problem ((1.66), (1.67)). When the initial deflection vanishes the solution of a circular thinplate with initial deflection is reduced to the solution of the problems of the nonlinear bending of a circular thin plate ^[6]. If the initial deflection is largish and the signs of the initial deflection with the intensity of the transverse load are opposite, when the intensity of the transverse load reaches a certain value, the circular thin plate with initial deflection should produce the Jumping phenomenon^[8].

Combined Longitudinal with Lateral Bending of Rectangular Plates Supported at Points of Corners

Cheng Xiang-sheng

1987, 8(5): 445-452.

Abstract(1464) PDF(624)

Abstract:
This paper discusses the problems of combined longitudinal with lateral bending of rectangular plates which are supported at four points of corners by means of the yariational calculus. In the text the lateral bending and the stability of thin plates are also treated respectively.

On Shock Layer Method for the Hypersonic Flow Problems

Yuan Yi-wu

1987, 8(5): 453-462.

Abstract(1916) PDF(552)

Abstract:
Chernyi's series method is not proper for the case that(γ-l)/(γ+l)<<2/(γ+1)(M²sin²β)(γ=c_p/c_v-adiabatic index number, M-Much number, shock incidence). In this paper, we only suppose that in the neighbour of the shock, there exists a shock layer in which the density of the gas is very big, but we do not remove the case that (γ-1)/(γ+1)<<2/(γ+1)(M²sin²β).

Study on the Characteristic of the Spray Angle in Pressure Swirl Spray Atomisation

Lu Ding-yuan

1987, 8(5): 463-472.

Abstract(1782) PDF(560)

Abstract:
Based on the suggested atomisation theory for the swirl spray conical film, the formula for the spray angle characteristic of pressure swirl spray atomisation θ=tg^-12·(1-φ) is derived from the relation of acting forces in swirl spray.The spray angle characteristics of swirl spray are worked out with various formulas and compared with actual test data. The results show that the derived formulas for spray angle in this article agree comparatively well with the results from experiments, and that the expressions are simple. They are of definite value in practice.