应用数学和力学

1997 Vol. 18, No. 8

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Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology

Ding Xieping, Wang Fan

1997, 18(8): 669-684.

Abstract(2128) PDF(444)

Abstract:
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 random comparison resultsfor these systems of random equations relative to weak topotogy in Banach 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

Xu Shoudong, Wu Wangyi

1997, 18(8): 685-693.

Abstract(1704) PDF(443)

Abstract:
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-accurate monotonous 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 specialcon sideration on the information from neighboring elements.Examples show that the new scheme can eliminate oscillations near strong shocks obviously.

General Solution of a 2-D Weak Singular Integral Equation with Constraint and Its Applications

Yun Tianquan

1997, 18(8): 695-701.

Abstract(2054) PDF(442)

Abstract:
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,φ) is a local polar coordinatingwin origin at M(r,θ): (r,θ) 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 Q:g(ω)=F(r,θ)/[πkφ₀];g'=dg/dω,ω=N-r²sin²(θ+φ₀);φ₀ 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 with elastic half space, more simple and clear than Love's (1939), is given as an example of application.

General Solution of Plane Problem of Piezoelectric Media Expressed by“Harmonic Functions”

Ding Haojiang, Wang Guoqing, Chen Weiqiu

1997, 18(8): 703-710.

Abstract(2279) PDF(700)

Abstract:
First based on the basic equations of two-dimensional piezoelec troelasticity,adisplacement function is introduced and the general solution is then derived Utilizing the generalized Almansi's theorem. the general solution is so simplified that allphysical quantities can be expressed by three "harmonic functions".Second,solutions of 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 of point forces and point charge acting on the line boundary of a piezoelectric half-plane.

The Cut-and-Try Method in Determining the Saturate Spacing of Transverse Cracks of Composite Laminates

Mao Huiyong, Jiang Yongqiu, Ye Lin

1997, 18(8): 711-716.

Abstract(1852) PDF(410)

Abstract:
In this Paper, the saturate spacing of transverse cracks of the 90°ply is originally calculated 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): 717-724.

Abstract(2215) PDF(463)

Abstract:
In this paper some theorems on fixed points of pair of asymptotically regular mappings 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 H^p,k for 1[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

Shen Pengcheng, He Peixiang

1997, 18(8): 725-733.

Abstract(2096) PDF(536)

Abstract:
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

Lin Wenxian

1997, 18(8): 735-745.

Abstract(1902) PDF(661)

Abstract:
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 as well. At the sameime. some sufficient conditions for oscillatory solutions are also established.

Asynchronous Relaxed Iterative Methods for Solving Linear Systems of Equations

Gu Tongxiang

1997, 18(8): 747-751.

Abstract(2052) PDF(470)

Abstract:
In this paper, the asynchronous versions of classical iterative methods for solving linear 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 of convergence than that in [3] is obtained.

Scattering of Plane SH-Waves on Semi-Canyon Topography of Arbitrary Shape with Linging in Anisotropic Media

Han Feng, Liu Diankui

1997, 18(8): 753-761.

Abstract(1979) PDF(557)

Abstract:
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 arbitrary shape into a cylindrical canyon in full-space.Moreover,it is far practical in engineering 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.