应用数学和力学

1999 Vol. 20, No. 3

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Reciprocal Theorem Method for the Forced Vibration of Elastic Thick Rectangular Plates

Li Huijian, Fu Baolian, Tan Wenfeng

1998, 19(2): 175-188.

Abstract(2115) PDF(599)

Abstract:

In this paper, reciprocal theorem method( RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory.The paper derives the dynamic basic solution of thick rectangular plates; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient andgeneral method for calculating the steady- state responses of forced vibration of thick rectangular plates.

Some Dynamical Properties of a Viscoelastic Cylindrical Shell

Ding Rui, Zhu Zhengyou, Cheng Changjun

1999, 20(3): 221-228.

Abstract(2048) PDF(659)

Abstract:
In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By synthetically using the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the parameter has effect on the stability of structure are obtained.

Theory and Algorithm of Optimal Control Solution to Dynamic Systme Parameters Identification (Ⅱ) Stochastic System Parameters Identification and Application Example

Wu Zhigang, Wang Benli, Ma Xingrui

1999, 20(3): 229-234.

Abstract(2263) PDF(753)

Abstract:
Based on the contents of part(Ⅰ) and stochastic optimal control theory, the concept of optimal control solution to parameters identification of stochastic dynamic system is discussed at first. For the completeness of the theory developed in this paper and part (Ⅰ), then the procedure of es tablishing Hamilton-Jacobi-Bellman (HJB) equations of parameters identification problem is present ed. And then, parameters identification algorithm of stochastic dynamic system is introduced. At last, an application example-local nonlinear parameters identification of dynamic systemis presented.

Construction of Wavelet Bases with Vanishing Movement

Peng Ruiren, Chen Jiming, Peng Kang

1999, 20(3): 235-240.

Abstract(2208) PDF(676)

Abstract:
A kind of mother wavelet with good properties is constructed for any N≥2, which is di-f ferentiable for N times, converges to zero at the order of O|t|^-N(|t|→∞) and has N-2 order of vanishing movement and some property of symmetry meanwhile. A computation example for N=4 is also given.

The Unified Theory of Elastic-Viscosic-Plastic Theory of Solids

Jin Wenlu

1999, 20(3): 241-248.

Abstract(2184) PDF(699)

Abstract:
In this paper, unified elastic-viscosic-plastic theory which can compute the change of elastic, viscosic and plastic situation of each point in the body is suggested. The theory is based on the laws of thermodynamics and the pseudo elastic postulate. In the paper, the constitutive equations and variational principles are deduced. From which the finite element method of both space and time may be esily formulated. Note that, by choosing the material parameters properly, the plastic constitutive equations currently used may be given.

Variational Principles of Fluid Full-Filled Elastic Solids

Shi Zhifei, Huang Shuping, Zhang Zimao

1999, 20(3): 249-255.

Abstract(2691) PDF(626)

Abstract:
The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable,four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.

On the Arbitrary Difference Precise Integration Method and Its Numerical Stability

Qiang Shizhong, Wang Xiaoguo, Tang Maolin, Liu Min

1999, 20(3): 256-262.

Abstract(2314) PDF(836)

Abstract:
Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM further demonstrates advantages such as the abilities of better description of physical properties of inhomogeneous media and convenient treatment of various boundary conditions. The explicit integration schemes derived by ADPIM are proved unconditionally stable.

Relative Nonsymmetry Effects of the Super(Generalized) Nonlinear Velocity, Time of a Particle and Its Kinetic Formulae for Followed Body

Yang Wenxiong

1999, 20(3): 263-268.

Abstract(2148) PDF(646)

Abstract:
In the paper,it has been described the relative nonsymmetry effects of the super (generalized) nonlinear velocity, time of a particle and its kinetic formulae for the followed body when it moves with high velocity. The nonsymmetry effects can explain the problem appearing in the extention of the life time for the secondary cosmicray, μ mesons; they also can explain the controversial problem who is more young in the famous twin paradox. Finally, the followed body kinetic formulae for the particle have been founded.

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces

Zhou Haiyun

1999, 20(3): 269-276.

Abstract(2227) PDF(842)

Abstract:
:Let X be a real Banach space with a uniformly convex dual X^*. Let T :X y X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L≥1 and a strongly accretive constant k∈(0,1). Let {α_n},{β_n}. be two real sequence in [0,1] satisfying:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ) Set Sx=f-Tx+x Assume that be two sequences in X satisfying =o(β_n)与μ_n→0(n→∞).For arbitrary x₀∈X the iteration sequence {x_n} is defined by IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0) then {x_n converges strongly to the unique solution of the equation Tx=f A related result deals with iterative approximation of fixed points of φhemicontractive mappings.

Existence and Uniqueness of Solutions for Initial Value Problems of Second Order Ordinary Differential Equations in Banach Space

Hong Shihuang, Hu Shigeng

1999, 20(3): 277-285.

Abstract(2288) PDF(873)

Abstract:
In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.

Stress Effect Decay Estimates for Anisotropic Material in a Semi-Infinite Strip

Cai Chongxi, Lin Changhao

1999, 20(3): 286-294.

Abstract(1979) PDF(529)

Abstract:
In this paper, Saint-Venant's principle for anisotropic material in an end-loaded. semi-infinite elastic strip is established. Energy method is used to establish the lower bounds of the decay estimate of stress effect. An explicit estimate formula in terms of the elastic constants of the anisotropic materials is presented. Finally, a numerical example for an end-loaded, off-axis, graphite-epoxy strip is given to illustrate the results.

Derivation of The General Form of Elasticity Tensor of The Transverse Isotropic Material by Tensor Derivate

Chen Weiyi

1999, 20(3): 295-300.

Abstract(2389) PDF(1208)

Abstract:
In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two independent elasticity coefficients for isotropic elastic material and five for transverse isotropic elastic material can be seen more clearly.

Path-Independent J-Integral and Its Dual Form in Elastic-Plastic Solids with Finite Deformation

Wu Xiangfa, Fan Tianyou, Liu Changhe

1999, 20(3): 301-304.

Abstract(2495) PDF(847)

Abstract:
In this paper, based on energy variation principles of elastic-plastic solids, the path-independent J-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whoce testification is given there after.

A Reasonable Method for Constracting General Element DM4 of Thick and Thin Plate with Effectual and Realiable Numerical Solution

Yang Lian

1999, 20(3): 305-313.

Abstract(1922) PDF(514)

Abstract:
In this thesis,the interal relations between about shear looking, zero energy mode and patch test are studied, and a reasonable method provided for building general element of thick and thin plate with effectual and realiable numerical solution.

Existence of Solutions for Parabolic Type Evolution Differential Inclusions and the Property of the Solution Set

Wang Zhihua

1999, 20(3): 314-318.

Abstract(1885) PDF(769)

Abstract:
In this paper, parabolic type differential inclusions with time dependenoe are discussed and this problem is related to the study of the nonlinear distributed parameter control systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P.Aubin et al are generalized and improved.

Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions

Yin Xiaochun

1999, 20(3): 319-324.

Abstract(2409) PDF(858)

Abstract:
In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of several contact hollow cylinders can be replaced by the frequency equation of a single hollow cylinder,so that the solving process is greatly simplified. Some recursion formulae of Bessel functions are derived from such practice problems as well.

Damage Theory for Polymetric Material

Huang Xicheng

1999, 20(3): 325-329.

Abstract(2204) PDF(780)

Abstract:
In this paper,the effects of external environment such as corrosion medium,radiation and non-consistent materials on deformation of polymers are discussed. Damage constitutive equations for non-linear elastic and non-linear viscoelastic polymers and a variational principle for viscoelastic damage are also given.