应用数学和力学

1998 Vol. 19, No. 3

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Simulation of Typhoon’s Anomalous Track(Ⅰ)——Rankine Vortex Model

Lin Mian, Li Jiachun, Li Li

1998, 19(3): 189-194.

Abstract(2623) PDF(667)

Abstract:
This paper proposes a method for simulating symmetric and asymmetric typhoon by using Rankine vortex model.Considering similarity between tropical cyclone and the Rankine vortex,the paper has qualitatively discussed the feasilility of the methods.In order to decide quantitatively Rankine vortex's parameters to simulate typhoon's structure,the paper has dealt with TCM data for Yancy Typhoon(9012) as initial fields.These results are considered as a foundation for further studying typhoon motion by CD approach.

Taylor Polynomial Stepwise Refinement Algorithm for Lie and High Symmetries of Partial Differential Equations

Zhang Hongqing, Tang Limin, Chao Lu

1998, 19(3): 195-201.

Abstract(2486) PDF(917)

Abstract:
In this article,based on the Taylor expansions of generating functions and stepwise refinement procedure,authors suggest a algorithm for finding the Lie and high(generalized)symmetries of partial differential equations(PDEs).This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution.So,it reduces significantly the difficulties of the problem and raise computing efficiency.The whole procedure of the algorithm is carried out automatically by using any computer algebra system.In general,this algorithm can yields many more important symmetries for PDEs.

Wavelet Analysis in Testing Signal

Zhang Xiangwei, Luo Shaoming, Shigiru Nakagini

1998, 19(3): 203-207.

Abstract(2271) PDF(769)

Abstract:
In this paper,Wavelet Analysis Method(WAM)is introduced to analyse the non-stationary, shock signals.The theory and construction method of wavelet,the fast algorithms of wavelet analysis are presented.As an example,the gear testing signal has be analysed by WAM,and the results of WAM are compared with that of Fourier spectrum.The advantages of WAM are clearly shown.

Snap-Buckling of Dished Shallow Shells under Line Loads

Liu Dong, Chen Shanlin

1998, 19(3): 209-216.

Abstract(2165) PDF(474)

Abstract:
A theoretical analysis is presented for the snap-buckling behavior of dished shallow shells under axisymmetric distributed line loads.The second approximate formulae of elastic behavior of dished shallow shells with various boundary conditions are qiven,and effects of geometrical parameters γ,β and k on non-linear behavior are discussed.

Identification of Qusi-Static Displacement for Constitutive Models of Viscoelasticity

Yang Haitian, Wu Ruifeng, Zhang Qun

1998, 19(3): 217-221.

Abstract(1990) PDF(519)

Abstract:
An explicit relation between constitutive parameters and qusi-static displacement of viscoelasticity is derived under a kind of boundary condition,and an iterative form of optimized identification is presented.Viscoelastic constitutive models are identified from a two order differential model,and effects of information errors on results of inverse analysis are discussed.

Spherical Wave Propagation in Satuated Soils

Xu Changjie, Wu Shiming

1998, 19(3): 222-231.

Abstract(2304) PDF(468)

Abstract:
Based on the generally adopted soil model for engineering,ananalytic solution of spherical wave propagation problem in a special case for an equally pressurized spherical cavity in saturated space by Laplace transfo rmation which is compared with that of the same problem in a onep-hase elastic space.The influence of fluid on dynamic response of saturated soil is examined.The authors propose an effective way for dy namic analysis of under ground structure.

Panderivative Blown-Up of Ground Temperature and Predicting Earthquake

Li Chao, Ouyang Shoucheng, Tang Maocang

1998, 19(3): 233-241.

Abstract(1902) PDF(513)

Abstract:
According to the blown-up theory(described in references[1,2])for nonlinear dynamic system on the relationship of general pansystem transformation,optimsation and panderivative blown-up,by means of blown-up theory,we demonstrate that the blown-up of nonlinear heat conductive equation is similar to the evolution of observational ground temperature ‘flow'.in this paper.And a successful simulation of Tang Shan Earthquake in 1976 has been given.The result of simulation indicates that the blown-up of ground temperature-flow.around earthquake can be applied to predict earthquake. As for Tang Shan Earthquake,the predicting time is about five months. If ground temperat ure ‘flow'.that embodies the earth's crust satisfies the unintegral panderivative equation,we can demonstrate its mechanism and forecast earthquake with enough information.

The Fractal Structure of Attractor for the Generalized Kuramoto-Sivashinsky Equations

Dao Zhengde, Guo Boling, Lin Guoguang

1998, 19(3): 243-256.

Abstract(1934) PDF(543)

Abstract:
In this paper,the g eneralized Kuramoto-Sivashinsky e quations(GKS)with periodic initial boundar y value pr oblem are consider ed and the constr uction o f ine rtial sets in space H² is given. Furthemore,this paper gives and proves the fractal structure of attractors for GKS equations,and find out an exponentially approxim ating sequence of compact fractal localizing sets of the attractors, the sere sults sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in[1,3,5,7],which describe a kind of geometrical structure of the attractors.

Property Degradation of Anisotropic Composite Laminates with Matrix Cracking(Ⅰ)——Constitutive Relation Developing for (θ_m/90_n)_s Cracked Laminates by Stiffness Partition

Hua Yu, Wang Xingguo, Li Zhengneng

1998, 19(3): 257-265.

Abstract(2118) PDF(581)

Abstract:
The study on property degradation of damaged composite laminates is extended to anisotropic laminates with matrix cracking.In(Ⅰ)of the paper,an idea of "stiffness patition" is proposed to deal with the puzzle that the in-plane normal response is coupled with the shear response of the laminates.For(θ_m/90_n)_s laminates containing transversely cracked layers under general in-plane loading,the constitutive relations are derived and the effective stiffnesses are expressed as the function of crack density.

M-P Inverse Topological Variation Method of Finite Element Structures

Chen Suhuan, Liang Ping, Han Wanzhi

1998, 19(3): 267-278.

Abstract(2184) PDF(562)

Abstract:
Using Moore-Penrose inverse theory,a set of formulations for calculating the static responses of a changed finite element structure are given in this paper.Using these formulations in struct ural analysis may eliminate the need of assembling the stiffness matrix and solving a set of simultaneous equations.