Applied Mathematics and Mechanics (English Edition)

THE GROWTH OF THE VOID IN A HYPERELASTIC RECTANGULAR PLATE UNDER A UNIAXIAL EXTENSION

程昌钧;尚新春

1997, 18(7): 615-621.

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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 exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.

THE PARAMETER PERTURBATION METHOD ON ELASTIC WAVE EQUATION IN INHOMOGENEOUS MEDIUM

牛玉清;马兴瑞;黄文虎

1997, 18(7): 623-628.

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In this paper, the medium parameters of the elastic wave equation ininhomogeneous medium are rewritten by introducing the referential variables and theperturbational variables, and the wave equation whose sources are the mediumparameter perturbational term in homogeneous medtam is obtained By usingthe Green function theory, the integral equation of the perturbational parmeters isobtained. 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, thecharacteristics of wave field in inhomogeneous medium are obtained. The resultsconform 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

刘殿魁;胡超

1997, 18(7): 629-646.

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In this paper a complex variable analytic method for solving stress concentrationsin the circular cylindrical shell is proposed. The problem to be solved can besummarized into the solution of an infinite algebraic equation series. The solution canbe normal and effective by means of this method. Nunerical results for stressconcentrations 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

李航;刘志强

1997, 18(7): 647-655.

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This paper discusses the analytic solutions of the diffusion equation.for themovement of water in unsaturated soil. Firstly, according to the experience relationbetween the diffusivity "D(θ)" and water content in soil "θ",and through variablesubstitution, 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 analyticfunction of θ(x. t) is obtained, which is verified by the experiment of water flowthrough unsaturated soil.

THE ASYMPTOTIC THEORY OF SEMILINEAR PERTURBED TELEGRAPH EQUATION AND ITS APPLICATION

赖绍永

1997, 18(7): 657-662.

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This paper is devoted to studying the asymptotic theory of initial value problemsfor a semilinear perturbed telegraph equation. The asymptotic theory and validity offormal approximations are constructed on long timescale O(|ε|^-1). Asan application ofthe 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

钱仍勣

1997, 18(7): 663-665.

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The variational functional of the Hellinger-Reissner variational principle for thelarge displacement problem of a thin shallow shell with an arbitrary shape is firstestablished. Then the functional of the modifed principle suitable for the finite elementmethod is derived. In the.functional only two independent variables, the deflection wand the stress function F are inchuded. The displacement expressions in the middlesurface on the boundary of the shell is also derived by means of the previous twovariables.

GENERALIZED STRUCTURE OF LAX REPRESENTATIONS FOR NONLINEAR EVOLUTION EQUATION

乔志军

1997, 18(7): 671-677.

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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-isospectralhierarchy. Under this form a generalized structure of Lax representations for thehierarchy of NLEEs is this presented. As a concrete example. the Levi-hierarchy ofevolution equations are discussed at the end of this paper.

PERTURBATIONAL SOLUTIONS FOR FUZZY-STOCHASTIC FINITE ELEMENT EQUILIBRIUM EQUATIONS (FSFEEE)

吕恩林

1997, 18(7): 679-687.

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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 derivedfrom the Small-parameter perturbation theory. The computational formulae of statisticalcharacteristic of the fuzzy random displacements, the fuzzy random strains and thefuzzy random stresses are also deduced in detail.

ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENING CERAMICS(Ⅱ)

张浠;叶裕恭

1997, 18(7): 689-696.

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Based on a constitutive law which includes the shear components oftransformation plasticity. the asymptotic solutions to near-tip fields of plane-strainmode I steadity propagating cracks in rransformed ceramics are obtained for the caseof linear isotropic hardening. The Stress singularity. the distributions of stresses andvelocities at the crack tip are determmed for various material parameters. The factorsinfluencing the near-tip fields are discussed in detail.

THE BENDING OF SET SQUARES WITH ONE FREE OBLIQUE EDGE UNDER A CONCENTRATED LOAD

边宇虹

1997, 18(7): 697-706.

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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

杨孝平;周叔子;李光耀

1997, 18(7): 707-720.

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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 problemwhich had mixed boundary conditions, the regularity of the solutions was established

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