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(1976) 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 ...

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(2063) 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 mechanic...

The Parametric Variational Principle for Perzyna Model in Viscoplasticity

Zeng Pan, Zhong Wan-xie

1991, 12(5): 409-414.

Abstract(3178) PDF(670)

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, ...

On the Nonlinear Stability Behaviour of Distorted Plane Couette Flow

Zhou Zhe-wei

1991, 12(5): 415-419.

Abstract(2400) 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(2298) 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,...

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(2128) 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 loa...

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(2319) 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(2233) 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(3243) 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 ...

Generalized Minimax Inequalities and Fixed Point Theorems

Ma Yi-hai, Zhang Fu-bao

1991, 12(5): 465-472.

Abstract(2182) 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 the...

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

Li Lin-sen

1991, 12(5): 473-478.

Abstract(2169) 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 ...

Numerical Studies of the Cold Flow Field in Model Combustion Chambers

Jia Shao-bo, Huang Jie

1991, 12(5): 479-484.

Abstract(1894) 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 c...