Asymptotic solution for coupled heat and mass transfer during the solidification of high water content materials

This paper focuses on obtaining an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials. It is found that a complicated function involved in governing equations can be approached by Taylor polynomials unlimitedly, which leads to the simplification of governing equations. The unknown functions involved in governing equations can then be approximated by Chebyshev polynomials. The coefficients of Chebyshev polynomials are determined and an asymptotic solution is obtained. With the asymptotic solution, the dehydration and freezing fronts of materials are evaluated easily, and are consistent with numerical results obtained by using an explicit finite difference method.     

Numerical Model of Storm Surge and Inundation in Bohai Bay

A two-dimensional numerical model of extratropical storm surge and inundation in Bohai Bay was built based on the unsteady flow Navier-Stokes equations. The model included two sections, one was for the simulation of storm surge tidal level and the other for the simulation of storm surge inundation in the coastal area. While simulating the storm surge tidal level, the alternating direction implicit (ADI) method was applied to dispersing and solving 2D storm surge equations. In the simulation of storm surge inundation, the 2D unsteady flow equations were dispersed and solved using the structureless grids of finite volume method (FVM). A coupling calculation mode of the process of inundation and storm surge tidal level variation was proposed, therefore the storm surge inundation process and area could be calculated while simulating and forecasting the process of storm surge tidal setup. Furthermore, an extratropical storm surge and inundation in Bohai Bay were simulated using this numerical model. Simulation results are in good agreement with the measured data, which shows that this numerical model provides a new method of simulating and forecasting storm surge and inundation in Bohai Bay.     

Bifurcation and chaos of a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields

We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the expressions of electromagnetic forces, the vibration equations are derived for the mechanical loading in a steady transverse magnetic field. Using the Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponent diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained.     

可修冗余系统密度演化方程的算子半群

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution,the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations,called density evolution equations.It was proved that the time-dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi-group method.In this proof,it is not necessary to suppose that the repair rate function is bounded.The technique of the proof is valuable for many density evolution equatons.     

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincaré(LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equations are converted into a group of linear ordinary differential equations by introducing a set of simple transformations.An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modified method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation,and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.     

Local data analysis for eliminating end restraint of triaxial specimen

A data processing method was proposed for eliminating the end restraint in triaxial tests of soil. A digital image processing method was used to calculate the local deformations and local stresses for any region on the surface of triaxial soil specimens. The principle and implementation of this digital image processing method were introduced as well as the calculation method for local mechanical properties of soil specimens. Comparisons were made between the test results calculated by the data from both the entire specimen and local regions, and it was found that the deformations were more uniform in the middle region compared with the entire specimen. In order to quantify the nonuniform characteristic of deformation, the non-uniformity coefficients of strain were defined and calculated. Traditional and end-lubricated triaxial tests were conducted under the same condition to investigate the effects of using local region data for deformation calculation on eliminating the end restraint of specimens. After the statistical analysis of all test results, it was concluded that for the tested soil specimen with the size of 39.1 mm × 80 ram, the utilization of the middle 35 mm region of traditional specimens in data processing had a better effect on eliminating end restraint compared with end lubrication. Furthermore, the local data analysis in this paper was validated through the comparisons with the test results from other researchers.     

估计第二类Fredholm 积分方程特征值的函数值部分Pad´e-型逼近方法

Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation.     

Dynamic response analysis of a moored crane-ship with a flexible boom

The dynamic response of moored crane-ship is studied. Governing equations for the dynamic response of a crane-ship coupled with the pendulum motion of the payload are derived based on Lagrange＇s equations. The boom is modeled based on finite element method, while the payload is modeled as a planar pendulum of point mass. The dynamic response was studied using numerical method. The calculation results show that the large-amplitude responses occur at wave periods near the natural period of the payload. Load swing angle is smaller for crane-ship with flexible boom, in comparison with rigid boom. The ship surge motions have large vibrations for crane-ship with flexible boom, which were not observed for a rigid boom. The analysis identifies the significance of key parameters and reveals how the system design can be adjusted to avoid critical conditions.     

半解析法求解含轴向浅槽复合材料圆柱壳的非线性动力响应及屈曲问题

The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.     

Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces

In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^ in Banach spaces. By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.     

关于Legendre多项式的一些恒等式

利用初等方法研究了多项式的性质，得到了一组关于多项式的卷积公式和Gegenbauer，L.多项式的一个表达式．     

Legendre矩的缩放不变量研究

如果图像大小变化,发现Legendre矩本身就近似具有缩放不变性,实验表明它的自身的不变性甚至优于缩放不变量;说明了Legendre的缩放不变量具有反转不变性是因为Legendre多项式只有偶数项的幂级数．     

双平均亚洲期权定价问题的Legendre谱方法

Abstract In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by     

解第二类非线性Fredholm积分方程的小波Galerkin方法

提出了利用Legendre小波解第二类非线性Fredholm积分方程的小波Galerkin近似方法.积分方程的非线性部分由在区间[a,b]上构造的Legendre小波进行逼近,而且将非线性积分方程化简为非线性积分方程组.给出的例子说明了此逼近方法的有效性和可操作性.     

第二类Volterra积分方程的一种特殊解法

研究了求解Volterra型积分方程的方法,重点介绍了基于谱方法解决Volterra型积分方程的一种新的数值解法,legendre配制法得到充分的应用,并进行了严格的误差分析,表明在核函数和原函数充分光滑时,数值误差是指数下降的.     

Chebyshev-Legendre method for discretizing optimal control problems

In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.     

SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS

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一类具高阶奇性解的完全奇异积分方程的直接解法

文章讨论了一类具有高阶奇异性解的完全奇异积分方程的直接求解问题.通过引入Hermite插值多项式,得到了这类奇异积分方程可解的充要条件和解的封闭形式,从而进一步扩大了完全奇异方程直接解法的求解范围.