应用数学和力学

General Solution for U-Shaped Bellows Overall-Bending Problems

Zhao Weiping, Guo ping, Huang Qian

2000, 21(4): 331-341.

Abstract(2877) PDF(794)

Abstract:
The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping,et al.and the solution for ring plates.The results evaluated in this paper are compared with those on EJMA(standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxin,et al.

On a New Algorithm of Constructing Solitary Wave Solutions for Systems of Nonlinear Evolution Equations in mathematical Physics

Yan Zhenya, Zhang Hongqing

2000, 21(4): 342-347.

Abstract(2084) PDF(649)

Abstract:
According to the improved sine-cosine method and Wu-elimination method,a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward.The algorithm has some conclusions which are better than what the hyperbolic function method known does and is simpler in use.With the aid of MATHEMATICA,the algorithm can be carried out in computer.

Abundance of Uenimodal Maps With Dense Critical Orbit and Prefixed Critical Orbit

Cao Yongluo, Wang Lanyu

2000, 21(4): 348-352.

Abstract(2471) PDF(527)

Abstract:
For the so-called quadratic family,it is proved that,there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E;it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.

Five Order Isotropic Descartes Tensor

Yan Dagui, Xu Jun, Yan Shang'an, Fu Shilu

2000, 21(4): 353-356.

Abstract(2145) PDF(561)

Abstract:
Five order isotropic descartes tensor and its existence theorem and representation problems are researched,then a general representation formula of five order isotropic descartes tensor is got.

Singular Integral Equations and Boundary Element Method of Cracks in Thermally Stressed Planar Solids

Xu Chunhui, Qin Taiyan, Hua Yunlong

2000, 21(4): 357-364.

Abstract(2194) PDF(531)

Abstract:
Using the method of the boundary integral equation,a set of singular integral equations of the heat transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived,and then its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method.Moreover,the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation,and the singular temperature gradients are exactly obtained.Finally,several typical examples are calculated.

Construction of High-Order Accuracy Implicit Residual Smoothing Schemes

Ni Migjiu, Xi Guang, Wang Shangjin

2000, 21(4): 365-372.

Abstract(2901) PDF(3381)

Abstract:
Referring to the construction way of Lax-Wendroff scheme,new IRS(Implicit Residual Smoothing) schemes have been developed for hyperbolic,parabolic and hyper-parabolic equations.These IRS schemes have 2nd-or 3rd-order time accuracy,and can extend the stability region of basic explicit time-stepping scheme greatly and thus can permit higher CFL number in the calculation of flow field.The central smoothing and upwind-bias smoothing techniques have been developed too.Based on one-dimensional linear model equation,it has been found that the scheme is unconditionally stable according to the von-Neumann analysis.The limitation of Dawes' method,which has been applied in turbomachinery widespreadly,has been discussed on solving steady flow and viscous flow.It is shown that stable solution of this method is not completely independent with the value of time step.In the end,numerical results by using IRS schemes and Dawes' method as well as TVD(total variation diminishing) scheme and four-stage Runge-Kutta technique are presented to verify the analytical conclusions.

A Crystallographic Model for the Orientation Dependence of Low Cyclic Fatigue Property of a Nickel-Base Single Crystal Superalloy

Yue Zhufeng, Tao Xiande, Ying Zeyong, Li Haiyan

2000, 21(4): 373-381.

Abstract(2573) PDF(944)

Abstract:
Fully reversed low cyclic fatigue(LCF) tests were conducted on [001],[012],[112],[011] and [11 4] oriented single crystals of nickel-based superalloy DD3 with different cyclic strain rates at 950℃.The cyclic strain rates were chosen as 1.0×10^-2,1.33×10^-3 and 0.33×10^-3s^-1.The octahedral slip systems were confirmed to be activated on all the specimens.The experimental result shows that the fatigue behavior depends on the crystallographic orientation and cyclic strain rate.Except [001] orientation specimens,it is found from the scanning electron microscopy(SEM) examination that there are typical fatigue striations on the fracture surfaces.These fatigue striations are made up of cracks.The width of the fatigue striations depends on the crystallographic orientation and varies with the total strain range.A simple linear relationship exists between the width and total shear strain range modified by an orientation and strain rate parameter.The nonconformity to the Schmid law of tensile/compressive flow stress and plastic behavior existed at 950℃,and an orientation and strain rate modified Lall-Chin-Pope(LCP) model was derived for the nonconformity.The influence of crystallographic orientation and cyclic strain rate on the LCF behavior can be predicted satisfactorily by the model.In terms of an orientation and strain rate modified total strain range,a model for fatigue life was proposed and used successfully to correlate the fatigue lives studied

General Failure Probability Simulation and Application for Multi-Mode

Lu Zhenzhou, Yue Zhufeng, Feng Yunwen

2000, 21(4): 382-388.

Abstract(2103) PDF(537)

Abstract:
A general failure probability simulation and deviation evaluation methods were presented for fuzzy safety state and fuzzy failure state.And the corresponding number integral method was simultaneously established.As the distribution of state variable and the membership of the state variable to the fuzzy safety set were normal,the general failure probability of the single failure mode had precise analytic solution,which was used to verify the precision of the presented methods.The results show that the evaluation of the simulation method convergences to the analytic solution with the number increase of the sampling.The above methods for the single failure mode was extended to the multi-mode by the expansion and probability principles.The presented methods were applied to the engineering problem.For the number of significant mode is not too many,the high precision solution can be given by the presented number simulation and number integral methods,which is illustrated by the engineering examples.In addition,the application scope of the methods was discussed.

Adjoint System Integrals for Optimal Space N-Impulse Transfer

Wu Yuliang

2000, 21(4): 389-392.

Abstract(2128) PDF(379)

Abstract:
The adjoint system integrals for time free,optimal N-impulse transfer during a firing period in 5-phase selected are derived.

4th Order Spline Wavelets on a Bounded Interval

Duan Jiwei, Li Qiguan

2000, 21(4): 393-401.

Abstract(2765) PDF(738)

Abstract:
The 4th order spline wavelets on a bounded interval are constructed by the 4th order truncated B-spline functions.These wavelets consist of inner and boundary wavelets.They are bases of wavelet space with finite dimensions.Any function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets.It plays an important role for numerical analysis of partial differential equations,signal processes,and other similar problems.

Parameter Identification of Dynamic Models Using a Bayes Approach

Li Shu, Zhuo Jiashou, Ren Qingwen

2000, 21(4): 402-408.

Abstract(2742) PDF(683)

Abstract:
The Bayesian method of statistical analysis has been applied to the parameter identification problem.A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies.This is based on the solution of an inverse generalized eigenvalue problem.The stochastic nature of test date is considered and a normal distribution is used for the measurement frequencies.An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure.A numerical example demonstrates the efficiency of the method.

Periodicity and Strict Oscillation for Generalized Lyness Equations

Li Xianyi, Xiao Gongfu

2000, 21(4): 409-414.

Abstract(2478) PDF(464)

Abstract:
A generalized Lyness equation is investigated as follows where a,b∈[0,∞) with a＋b＞0 and where the initial values x_-1,x₀ are arbitrary positive numbers.Some new results,mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq(*),are obtained.As an application,the results solve an open problem presented by G.Ladas.

Analytical Solution for Mode Ⅱ Dynamic Rupture of Standard Linear Viscoelastic Solid With Nonlinear Damping

Fan Jiashen

2000, 21(4): 415-423.

Abstract(2063) PDF(635)

Abstract:
Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid,this equation is a partial differential and integral equation.First,eliminating the integral term,a PDE of order three is obtained.Then,applying the small parameter expansion method,linearized asymptotic governing equation for each order of the small parameter is obtained.Dividing the order three PDE into an elastic part with known solution,the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one.The WKBJ method is still adopted to solve it analytically.

Passive Vibration Control of Spare Structure by Receptance Theory

Yan Tianhong, Zheng Gangtie, Huang Wenhu

2000, 21(4): 424-430.

Abstract(2271) PDF(514)

Abstract:
The vibration of three-dimensional frame structures was studied as receptance motion.A receptance model was constructed for passive vibration reduction.First,the universal receptance computational method suitable to any combination of boundary conditions was given,and then the way of passive damping-damping elements was analyzed,and a iterative approach to select optimal damping positions,whose dissipated power is larger than the others,was proposed based on the results of receptance analysis.The results show that,the receptance model is very stitable for local modification and analysis of structures.

Robust Stability for a Type of Uncertain Time-Delay Systems

Nian Xianhong

2000, 21(4): 431-436.

Abstract(2171) PDF(493)

Abstract:
Some new results for stability of uncertain time-delay systems are derived and the stability degree is also discussed.Some previous results for stability and robust stability of time-delay systems are improved.Lastly,examples are included to illustrate our results.

On the Critical Points of the Map

Yang Changsen

2000, 21(4): 437-440.

Abstract(2030) PDF(485)

Abstract:
Suppose A,B and C are the bounded linear operators on a Hilbert space H,when A has a generalized inverse A^- such that (AA^-)^*＝AA^- and B has a generalized inverse B^- such that (B^-B)^*＝B^-B, the general characteristic forms for the critical points of the map F_p:X→‖AXB-C‖_p^p(1<p<∞),have been obtained,it is a generalization for P.J.Maher result about p=2.Similarly,the same question has been discussed for several operators.

2000 Vol. 21, No. 4