应用数学和力学

1995 Vol. 16, No. 2

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A Further Study of the Theory of Elastic Circular Plates with Non-Kirchhoff-Love Assumptions

Chien Wei-zang, Ru Xue-ping

1995, 16(2): 95-106.

Abstract(2033) PDF(555)

Abstract:
Based on the general theory of elastic plates which abandons Kirchhoff-Love assunption in the classical theory.this paper establishes a first order approximation theory of elastic circular plates with non-Kirchhoff-Love assumption,and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clamped boundary under uniformly distributed load.By comparing with the classical solution of the thin circular plates,it is verified that the new solution is closer to the experiment results than the classical solution.By virtue of the new theory.the influence of thediameter-to-thickness ratio upon the precision of the classical theory is examined.

Curve Cracks Lylng along a Parabolic Curve in Anisotropic Body Hu Yuan-tai

Zhao Xing-hua

1995, 16(2): 107-116.

Abstract(1878) PDF(726)

Abstract:
A general solutions for the stress and displacement of curve cracks distributing along a parabolic curve Ω in an infinite homogeneous anisotropic medium subjected tounifrom loading a infinity have been given in this paper by using the Stroh's formalism and the mapping method.The solutions are valid not only for plane problems but also for antiplane problems and the problems whose inplane andantiplane deformations couple each other.A closed form solution for the stress and dispacement in the entire domain is obtained for one curve crack or two curve cracks along the parabolic curve.The simple explicit form solution for the stress intensity factors and the crack opening displacement are presented.

Hamiltonian systems in Elasticity and Their Variational Principles

Wang Zhi-guo, Tang Li-min

1995, 16(2): 117-122.

Abstract(2433) PDF(559)

Abstract:
As an inverse problem of Hamiltonian mechanics,a new Hamiltonian system in elasticity and its variational principle are derived from the basic equations of elasticity.

Topologicai Version of Section Theorems with Applications

Zhang Shi-sheng, Wu Xian

1995, 16(2): 123-131.

Abstract(1728) PDF(494)

Abstract:
In this paper some new types of KKM theorem and section theorems are given.As applications,the existence problems of solutions for three kinds of variational inequalities and fixed point problem for set-valued mapping have been siudied by usingthose results.The results presented in this paper improve and extend the main resultsin [1-19].

The Exact Solution for Thick Laminated Cantilever Cylindrical Shell

Fan Jia-rang, Ding Ke-wei

1995, 16(2): 133-147.

Abstract(1958) PDF(587)

Abstract:
Discarding any assumption regarding displacement or strers models,the state equation for orthotropy is established in a cylindrical system.The exact solution is presented for the statics of thick closed laminated cantilever cylindrical shells.Everyequation of elasticity can be satisfied and all the elastic constants are taken into account.Arbitrary precision of a desired order can be obtained.

Free Vibration and Stability of Moderate-Thick Cantilever Plates

Zhang Yin-yi

1995, 16(2): 149-154.

Abstract(1969) PDF(491)

Abstract:
By means of the constitution of the two displacement functions and the application of the least square method and the energy method this paper gives the Reissner approximate solutions of the free vibration and the stability for the moderate-thick cantilever rectangular plate.

A Variational Analytical Approach to Time Dependent Flow of Oldroyd B Fluid in Circular Tube

Han Shi-fang, H. Ramkissoon

1995, 16(2): 155-164.

Abstract(2161) PDF(532)

Abstract:
In the present investigation the time dependent flow of an Oldroyd fluid B in a horizontal eylindrical pipe is stuided by the variational analytical approach developed by author.The tome dependent problem is mathematically reduced to a partial differential equation of third order.Using the improved variational approach due to Kantorovich the partial differential equation can be reduced to a system of ordinary differential equations for different approximations.The ordinary differential equations are solved by the method of the Laplace transform which is led to an analytical form of the solutions.

Some NeW Fixed point Theorems in Probabilistic Metric Spaces

Zhu Chuan-xi

1995, 16(2): 165-171.

Abstract(2267) PDF(711)

Abstract:
In this paper,we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Mean while,some famous fixed point theorems are generalized in probabilistic metric spaces,such as fixed point theorem of Schauder,Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space.And fixed point theorem of Altman is also generalized in the Z-M-PN space.

Spectral Method for Semilinear Parabolic Integrodifferential Equations

Liu Xiao-qing, Wu Sheng-chang

1995, 16(2): 173-179.

Abstract(1815) PDF(482)

Abstract:
Based on the discussion of the semi discretization of a parabolic equation with a semilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.

A Study of the Construction of Lyapunov Function for a Class of Fourth Order Nonlinear Systems

Liang Zai-zhong

1995, 16(2): 181-188.

Abstract(2375) PDF(678)

Abstract:
In the paper Lyapunov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.