应用数学和力学

1997 Vol. 18, No. 7

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The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension

Cheng Changjun, Shang Xinchun

1997, 18(7): 573-578.

Abstract(2019) PDF(546)

Abstract:
In the presenl paper, the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the existence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelustic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation iS also nunterically computed and analysed.

The Parameter Perturbation Method on Elastic Wave Equation in inhomogeneous Medium

Niu Yuqing, Ma Xingrui, Huang Wenhu

1997, 18(7): 579-584.

Abstract(2209) PDF(634)

Abstract:
In this paper, the medium parameters of the elastic wave equation in inhomogeneous medium are rewritten by introducing the referential variables and the perturbational variables, and the wave equation whose sources are the medium parameter perturbational term in homogeneous medtam is obtained By usingthe Green function theory, the integral equation of the perturbational parmeters is obtained. Then the displacement field in homogeneous medium is considered the resultof the first iteration, and the displacement fisld is solved by this integral equation.When the perturbations of medium paranteters are about 50 percent, this method cansolve the displacement ficld effectirely. From the analysis of the numerical results, the characteristics of wave field in inhomogeneous medium are obtained. The results conform with the local principles of wave, function in inhomogeneous medium.

The General Solution for the Stress Problem of Circular Cylindrical Shells with an Arbitrary Cutout

Liu Diankui, Hu Chao

1997, 18(7): 585-602.

Abstract(2571) PDF(608)

Abstract:
In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution canbe normal and effective by means of this method. Nunerical results for stress concentrations in the shell with a circular, elliplic cutout are graphically presented.

Almost Analytic Solutions and Their Tests of the Horizontal Diffusion Equation for the Movement of Water in Unsaturated Soil

Li Hang, Liu Zhiqiang

1997, 18(7): 603-610.

Abstract(2001) PDF(482)

Abstract:
This paper discusses the analytic solutions of the diffusion equation.for the movement of water in unsaturated soil. Firstly, according to the experience relation between the diffusivity "D(θ)" and water content in soil "θ",and through variable substitution, the original diffsion equation is converted into the form easy to solve.Then, the variables separution method together with the Boltzmann transform methodis used to find out the solution of the new partial differential equation. So the analytic function of θ(x,t) is obtained, which is verified by the experiment of water flow through unsaturated soil.

The Asymptoic Theory of Semilinear Perturbed Telegraph Equation and Its Application

Lai Shaoyong

1997, 18(7): 611-616.

Abstract(2163) PDF(625)

Abstract:
This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(|ε|^-1). Asan application of the asymptotic theory, the initial value problenis for a special telegraph equation arestudied and two asymptotic solutions of order O(|ε|^-1) are presented.

A Modified Hellinger-Reissner Variational Functional Including only Two Independent Variables for Large Displacement of Thin Shallow Shell

Qian Rengji

1997, 18(7): 617-624.

Abstract(2287) PDF(443)

Abstract:
The variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with an arbitrary shape is first established. Then the functional of the modifed principle suitable for the finite element method is derived. In the.functional only two independent variables, the deflection wand the stress function F are inchuded. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.

Generalized Structure of Lax Representations for Nonlinear Evolution Equation

Qiao Zhijun

1997, 18(7): 625-630.

Abstract(1947) PDF(431)

Abstract:
A new production form for a hierarchy of nonlinear evolution equations (NLEEs)is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is thus presented. As a concrete example. the Levi-hierarchy of evolution equations are discussed at the end of this paper.

Perturbational Solutions for Fuzzy-Stochastic Finite Element Equilibrium Equations (FSFEEE)

Lű Enlin

1997, 18(7): 631-638.

Abstract(2254) PDF(593)

Abstract:
In this paper. the random interval equilibrium equations (RIEE) is obtained by λ-level cutting the fuzzy-stochastic finite element equilibrium equations (FSFEEE).Based on the relations between the variables of equilibrium equations, solvting RIEE istransformed into solving two kinds of general random equilibrium equaltions (GREE).Then the recursive equations of evaluaing the random interval displacement is derived from the Small-parameter perturbation theory. The computational formulae of statistical characteristic of the fuzzy random displacements, the fuzzy random strains and thefuzzy random stresses are also deduced in detail.

Asymptotic Analysis of Plane-Strain ModeⅠSteady-State Crack Growth in Transformation Toughening Ceramics(Ⅱ)

Zhang Xi, Ye Yugong

1997, 18(7): 639-646.

Abstract(2207) PDF(449)

Abstract:
Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strainmode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The Stress singularity, the distributions of stresses and velocities at the crack tip are determmed for various material parameters. The factors influencing the near-tip fields are discussed in detail.

The Bending of Set-Squares with One Free Oblique Edge under a Concentrated Load

Bian Yuhong

1997, 18(7): 647-655.

Abstract(2352) PDF(577)

Abstract:
In the paper, the reciprocal theorem is applied to research on the bending of setsquare with one free oblique edge and two clamped edges under a concentrated loadacting at any point. This method is simpler and general.

On an Axially Symmetric Elastic-Plastic Torsion Problem

Yang Xiaoping, Zhou Shuzhi, Li Guangyao

1997, 18(7): 657-668.

Abstract(1938) PDF(448)

Abstract:
This paper discussed an axially symmetric elastic-plastic torsion problem. Invirtue of penalty method, reflection, boundaries, Bernstem estimate and reverse Holderinequality, on account of studying the corresponding complementary boundary problem which had mixed boundary conditions, the regularity of the solutions was established.