应用数学和力学

1996 Vol. 17, No. 2

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Existence Theorems of Solutions for Two-Point Boundary Value Problem of Second Order Ordinary DifferentialEquations in Banach Spaces

Zhang Shisheng, Wang Fan

1996, 17(2): 95-103.

Abstract(2145) PDF(550)

Abstract:
By using partial order method. some existing theorems of solutions for two-point bouniary value problem of second order ordinary differenlial equations in Banach spaces are given.

The Mathematical Models and Generalized Variational Principles of Nonlinear Analysis for Perforated Thin Plates

Cheng Changiun, Yang Xiao

1996, 17(2): 105-114.

Abstract(2210) PDF(572)

Abstract:
On foe basis of the Kirchoff-Kármán hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.

Analysis of Complex Stress Intensities for Cracked Laminates

Hu Hurang, Wu Chengping

1996, 17(2): 115-126.

Abstract(2221) PDF(600)

Abstract:
Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=1 approximation.

Forming Limit during Superglatic Deformation of Sheet Metals

Du Zhixiao, Li Miaoquan, Liu Mabao, Wu Shichun

1996, 17(2): 127-132.

Abstract(2124) PDF(672)

Abstract:
In the present paper, a thermo-viscoplastic damage potential and Hill's normal anisolropy(isotropy in plane).yield criterion to be quadratic in the stress components are combined to describe the interaction process of damage and instability during superplastic deformation, based on the kinetic equation for damoge during superplastic deformation and the deformation features of superplastic materials. The superplastic deformation process is devided into four Slages, namely, Stable, quasistable, Strain path drift to plane Strain and piane strain stages, and a damageinstability model during superplastic deformation of sheet metals is developed through numerical method. On the basis of the above results and taking the occurrence of localized inslability(dε₂=0) or the cavity volume fraction reaching the critical value(f_c) as a fracture criterion. the forming limit during superplastic deformation of sheet metals is predicted.

Power Vectors Combinatorial Vector Numbers and Its Theory of Functions

Yang Wenxiong

1996, 17(2): 133-138.

Abstract(2701) PDF(559)

Abstract:
This paper syggests the power vector and the vector power series. The vector power series is a "Combinatorial Vector Number" which is composed of a real number and a certain vector. Combinatorial rector variable and its functions have an important meaning. They have the fundamental operations of arithemetic too. From the theoretical analysis of functions for a combinatorial vector variable we would would know its function has the derivatives. the necessary and sufficient conditions. These conditions make up the charaders of "Hyperbolic equation" and its integralions.

Fixed Point with Orbital Diametral Function

B. K. Sharma, B. S. Thakur

1996, 17(2): 139-143.

Abstract(1807) PDF(520)

Abstract:
A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy & Roger's type contractive conditions. An example is given in its support.

On the Liapunov’s Stability of a Clamped Orthotropic Round Plate under Radial Axisymmetrical Impact Load

Jie Min

1996, 17(2): 145-149.

Abstract(2498) PDF(504)

Abstract:
Liapunov's 2nd method is applied to analyse the Stability of a ciamped poleorthotropic round plate acted by a radial axisymmetrical impact load on its periphery. The analysis is carried cut under the assumptions of small deflection and elasticity The impact load is supposed to have a step impulsive form. A sufficient stability condition is given.

The Property of Nonwandering Operator

Tian Lixin, Lu Dianchen

1996, 17(2): 151-156.

Abstract(1872) PDF(495)

Abstract:
In this paper. we stady the nonwandering operator, which is a linear operator with chaos character and is in intnite dimensionol linear space. We give the hypercyclic bacomposition on the compact set of nonwandering operators.

On Grammatical Complexity of a Class of Attractors

Lu Qinhe

1996, 17(2): 157-162.

Abstract(1847) PDF(449)

Abstract:
In this paper, we discuss the grammatical complexity of the Feigenbaum attractor and the Feigenbaum attractors in windows. We prove that the languages of these attractors are not conlexl-free language(CFL) but context-sensitive one(CSL).

Periodic Heat Transfer in the Fins with Variable Thermal Parameters

Yang Xiangxiang, He Hongzhou

1996, 17(2): 163-173.

Abstract(2037) PDF(554)

Abstract:
A Study is made on the periodic heat transfer in the fins with variable thermal parameters. The method of small parameter perturbation is adopted. Numerical calculation is solved noniteratively by shooting method and superposition method. For afin of certain shape with periodic change of fin base temperature, the heat transfer is influenced by the.following parameters. E-temperature function in relation to coefficient of thermal co1ductivity.N-characteristic parameter of finned heat trat transfer, ε-amplitude parameter of temperature.fluctuation, B-frequency parameter of temperature.fluctuation of the.fin, and the changing pattern of convective coefficient. The influences of these parameters on temperalure distribution, heat-flow rate. and fin efficiency are discussed. In addition to theoretical significance, the results are of practical significonce for engineering design.

Robust Control via State Feedback for a Class of Uncertain Bilinear Systems

Chen Songlin, Zhu Zuci

1996, 17(2): 175-179.

Abstract(2466) PDF(674)

Abstract:
This paper is concerned with the problem of designing a salabilizing controller for a class of uncertain bilinear systems. The uncertainties in the systems must satisfy matching condition and their bounds should be known. The so-called imyroved gpproach for stability analysis of nonlinear systems is used. Under some suitable assumptions a linear robust state feedback controller can be desikned. At last an illustralive example is demonstrated.

A Uniformly Difference Scheme of Singular Perturbation Problem for a Semilinear Ordinary Differential Equation with Mixed Boundary Value Condition

Bai Qingyuan, Lin Pengcheng

1996, 17(2): 181-188.

Abstract(2052) PDF(541)

Abstract:
In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an Il'in type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.