Applied Mathematics and Mechanics (English Edition)

SOLUTIONS FOR A SYSTEM OF NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS UNDER WEAK TOPOLOGY

丁协平;王凡

1997, 18(8): 721-737.

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In this paper. a Darbao type random fired point theorem for a system of lveak continuous random operators with random domain is first proved Then, by using thetheorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces aregiven. As applications, some existence theorems of weak random sohttions for the random Cauchy problem of a system of nonlinear random differential equations areobtained, as well as the existence of extremal random solutions and randomcomparison resultsfor these systems of random equations relative to weak topotogy inBanach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are mproved and generalized bythese theorems.

A HYBRID FINITE ELEMENT SCHEME FOR INVISCID SUPERSONIC FLOWS

徐守栋;吴望一

1997, 18(8): 739-748.

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A hybrid monotonous finite element algorithm is developed in the present paper,based on a second-order-accurate finite elment scheme and a first-order-accuratemonotonous one derived from the former by a unilateral lumping procedure in onedimensional case. The switch functions for the two dimensional Euler equation systemare constructed locally, based on the gradient of the flow field, with specialconsideration on the information from neighboring elements.Examples show that the ew scheme can eliminate oscillations near strong shocks obviously.

GENERAL SOLUTION OF A 2-D WEAK SINGULAR INTEGRAL EQUATION WITH CONSTRAINT AND ITS APPLICATIONS

云天铨

1997, 18(8): 749-755.

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In this paper, the solution, more general than [1], of a weak singular integral equation

subject to constraint

is found

where k and F are given continuous functions: (s,) is a local polar coordinatingwin origin at M(r,θ): (r) is the global polar coordinating with origin at O(0,0) F(r_*, θ)=c_*(const) is the boundary contour ∂Q of the considered range

and N are mean values. The solution shown in type (2.19) of [1] is a special case of theabove solution and only suits F(r,θ) = ω. The solution of a rigid cone contact withelastic half space. more simple and clear than Love’s (1939), is given as an example ofapplication.

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY “HARMONIC FUNCTIONS”

丁皓江;王国庆;陈伟球

1997, 18(8): 757-764.

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First based on the basic equations of two-dimensional piezoelectroelasticity,adisplacement function is introduced and the general solution is then derived Utilizing the generalized Almansis theorem. the general solution is so simplified that allphysical quantities can be expressed by three harmonic functions.Second,solutionsof problems of a wedge loaded by point forces and point charge at the apex are alsoobtained in the paper. These solutions can be degenerated to those of problems ofpoint forces and point charge acting on the line boundary of a piezoelectric half-plane.

765 THE CUT-AND-TRY METHOD IN DETERMINING THE SATURATE SPACING OF TRANSVERSE CRACKS OF COMPOSITE LAMINATES

茆会勇;蒋咏秋;叶林

1997, 18(8): 765-770.

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In this Paper, the saturate spacing of transverse cracks of the 90° ply is originallycalculated by the 3-D finite element method. Thus, a new approach is put forward for predicting the saturate spacing of transverse cracks.

FIXED POINTS OF A PAIR OF ASYMPTOTICALLY REGULAR MAPPINGS

B. K. Sharma;B. S. Thakur

1997, 18(8): 771-778.

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In this paper some theorems on fixed points of pair of asymptotically regularmappings in p-uniformly convex Banach space are proved For these mappings somefixed point theorems in a Hilbert space.in L^p spaces in Hardy spaces H^p and in Sobolev spaces Hpk for 1<P<+∞ and K≥0 are also established.Thus resultsof Gornicki[9,10] Kruppel[11,12] and others are extended.

ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

沈鹏程;何沛祥

1997, 18(8): 779-787.

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In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement ofthe plate on elastic foundation. The multivariable spline element equations are derived,based on the mixed variational principle. The analysis and calculations of bending,vibration and stability of the plates on elastic foundation are presented in the paper.Because the field functions of plate on elastic foundation are assumed independently,the precision of the field variables of bending moments and displacement is high.

OSCILLATORY BEHAVIOR FOR HIGH ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

林文贤

1997, 18(8): 789-800.

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In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure.It is found thatthe nonoscillatory sclutions only have two kinds on some conditions only have And necessaryconditions for the existence of each kind of nonoscillatory solutions are presented aswell. At the same ime. some sufficient conditions for oscillatory solutions are alsoestablished

ASYNCHRONOUS RELAXED ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

谷同祥

1997, 18(8): 801-806.

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In this paper, the asynchronous versions of classical iterative methods for solvinglinear systems of equations are considered. Sufficient conditions for convergence ofasynchronous relaxed processes are given for H-matrix by which not only therequirements of [3] on coefficient matrix are lowered, but also a larger region ofconvergence than that in [3] is obtained.

SCATTERING OF PLANE SH-WAVES ON SEMI-CANYON TOPOGRAPHY OF ARBITRARY SHAPE WITH LINGING IN ANISOTROPIC MEDIA

韩峰;刘殿魁

1997, 18(8): 807-816.

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The purpose of this paper is to use the conforma mapping method[1]to analyzeand evaluate the ground displacement and scattering of incident SH-waves, on thesurface of semi-canyon topography of arbitrary shape with lining in anisotropic media.The problem to be solved can be reduced to the solution of an infinite algebraicequation set by using the method of full-space expansion of Fourier progression Usingthe mapping function and scattering theory to solve problems due to semi-canyon topography with lining is just like mapping the semi-cylindrical canyon of arbitraryshape into a cylindrical canyon in full-space.Moreover,it is far practical inengineering practice.From the computational examples,it is obvious that the variation of displacement amplitudes on the surface near the canyon topography is rather sharp. especially when the freqencies of incident SH-waves increase.

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