应用数学和力学

1991 Vol. 12, No. 5

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Lagrange Equation of a Class of Nonholonomic Systems

Gao Pu-yun, Guo Zhong-heng

1991, 12(5): 397-400.

Abstract(1913) PDF(616)

Abstract:
Making use of conclusions from [1]: (1) d-δ operations are commutative; (2) the Appell-Chetaev condition restricting virtual displacements is superfluous, the present paper derives the Lagrange equation without multipliers for a class of first-order nonlinear nonholonomic dynamical systems by means of variational principle. This kind of equations is new.

On the Existence and Uniqueness of Solutions for a Class of Variational Inequalities with Applications to the Signorini Problem in Mechanics

Zhang Shi-sheng, Xiang Shu-wen

1991, 12(5): 401-407.

Abstract(1952) PDF(626)

Abstract:
In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we utilize the results presented in this paper to study the Signorini problem in mechanics.

The Parametric Variational Principle for Perzyna Model in Viscoplasticity

Zeng Pan, Zhong Wan-xie

1991, 12(5): 409-414.

Abstract(3002) PDF(664)

Abstract:
This paper presents the parametric variational principle for Perzyna model which is one of the main constitutive relations of viscoplasticity.The principle,by which the potential energy function is minimized under a constrained condition transformed by the constitutive relations of viscoplasticity, is free from the bound of Drucker's postulate of plastic flow and consequently suitable for solving the nonassociated plastic flow problems. Furthermore, the paper has proven the presented principle and discussed the creep problem.

On the Nonlinear Stability Behaviour of Distorted Plane Couette Flow

Zhou Zhe-wei

1991, 12(5): 415-419.

Abstract(2268) PDF(510)

Abstract:
This paper discusses the nonlinear stability behaviour of distorted plane Couette flow to 2-dimensional disturbances, and compares it with that of distorted plane Poiseuille flow. The results show that plane Couette flow is more unstable than plane Poiseuille flow to finite-amplitude disturbances.

An Application of Nonsymmetric Lax-Milgram Lemma to Nonassociated Plasticity

Gen Yan-ming

1991, 12(5): 421-428.

Abstract(2192) PDF(450)

Abstract:
Usually, in tha study of elasto-plasticity, the assoiated plasticity,i.e the plastic potential surface coincides with yield surface,is often used.However in practical problems, there are many materials which do not obey the associated plastic flow rule, For instance, the mechanical behavior of rock, concrete,etc.must be described by the. nonassociated flew rule when deformation occur, In This paper,by means of the nonsymmetric Laz-Milgram lemma, we shall discuss a series of important questions of the nonassociated plasticity in detail.

Nonlinear Bending of Shallow spherical Shells on the Pasternak Foundations

Lin Jia-ji, Xi Xing-zhong, Cao Ai-qua

1991, 12(5): 429-434.

Abstract(2033) PDF(698)

Abstract:
Based on Karman's nonlinear fundamental differential equations, the new approach, which combines modi/led iteration method with Galerkin's one, has been put forward to solve nonlinear bending of shallow spherical shell with concave base and clamped edges on the Pasternak foundation under uniform loads in this paper. Mathematical expression of load-deflection has been given; furthermore, results obtained are in good agreement with existent ones.

Periodic Solution to a kind of Singularly Perturbed Differential Equaions of Parabolic Type in Chemical Kinetics

Ni Ming-kang

1991, 12(5): 435-442.

Abstract(2212) PDF(432)

Abstract:
This paper deals with the problem on the periodic solution for the singularly perturbed differential equations of parabolic type originating from chemical kinetics in stratified media, A uniformly valid asymptotic solution is constructed and the related asymptotic estimate is given.

Buckiing and Post-Buckling of Annular Plates under Non-Axisymmetric P!ane Edge Forces

Cheng Chang-jun, Yang Xiao

1991, 12(5): 443-454.

Abstract(2137) PDF(414)

Abstract:
On the basis of both the general theory [1,2] and the finite element method [4] of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.

Solution of the Plane Stress Problems of Strain-Hardening Materials Described by Power-Law Using the Complex Pseudo-Stress Function

Wang Zi-kun, Wei Xue-xia, Gao Xin-liu

1991, 12(5): 455-464.

Abstract(3139) PDF(408)

Abstract:
In the present paper, the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-called complex pseudo-stress function, which makes it possible to solve the elastic-plastic plane stress problems of strain hardening materials described by power-law using the complex variable function method like that in the linear elasticity theory. By using this general method, the close-formed analytical solutions for the stress, strain and displacement components of the plane stress problems of power-law materials is deduced in the paper, which can also be used to solve the elasto-plastic plane stress problems of strain-hardening materials other than that described by power-law. As an example, the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved by using this method, the results of which are compared with those of a known asymptotic analytical solution obtained by the perturbation method.

Generalized Minimax Inequalities and Fixed Point Theorems

Ma Yi-hai, Zhang Fu-bao

1991, 12(5): 465-472.

Abstract(2081) PDF(361)

Abstract:
Recently, many authors^[1,3] have generalized the famous Ky Fan's minimax inequality. In this paper, we put forward T-diagonal convexity (concavity) conditions and develop the main results in this respect. Next, we discuss some fixed point problems, and generalize the Fan-Glicksberg's fixed point theorem^[14].

The Lifetime of an Artificial Satellite Moving in Nonuniform Rotating Atmosphere and instantaneous Circle Orbit

Li Lin-sen

1991, 12(5): 473-478.

Abstract(2091) PDF(393)

Abstract:
The lifetime of an artificial satellite moving in the circular orbit under the action of nonuniform rotating atmospheric drag is studied from an energy point of view in this paper. The angular velocity of atmospheric rotation decreases with height according to hydrodynamics. The atmospheric density decreases with height according to the exponential formula. The expression for the lifetime of a satellite in the instantaneous circular orbit in the above-mentioned rotating atmospheric model is derived, and the numerical estimation for the lifetime of a concrete satellite has been made. The result shows clearly that the satellite lifetime calculated by this paper is shorter than that calculated by the uniform rotating atmospheric model.

Numerical Studies of the Cold Flow Field in Model Combustion Chambers

Jia Shao-bo, Huang Jie

1991, 12(5): 479-484.

Abstract(1785) PDF(393)

Abstract:
Numerical analyses of the cold turbulent flow in model combustion chambers were made by using turbulent model. The hybrid difference scheme and SNIP method were employed. Numerical solutions for retouchmenl length and velocity distributions were obtained in the recirculating zone of the combustion chambers. The calculation results were in fairly good agreement with the reported experimental data. The work presented in this paper was a basic part of the calculation model of sudden-enlarged combustion chambers.