Streamline upwind finite element method using 6-node triangular element with adaptive remeshing technique for convective-diffusion problems

A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.     

Improved precise integration method for differential Riccati equation

An improved precise integration method(IPIM) for solving the differential Riccati equation(DRE) is presented.The solution to the DRE is connected with the exponential of a Hamiltonian matrix,and the precise integration method(PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix.The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE.Based on the error analysis,the criterion for choosing two parameters of the PIM is given.Three kinds of IPIMs for solving the DRE are proposed.The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.     

A FINITE DIFFERENCE METHOD FOR SIMULATING TRANSVERSE VIBRATIONS OF AN AXIALLY MOVING VISCOELASTIC STRING

A finite difference method is presented to simulate transverse vibrations of an axially moving string.By discretizing the governing equation and the equation of stress- strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two explicit difference schemes can be calculated alternatively, which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors,O(Δt~2 Δx~2).It also shows quite good stability for small initial values.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results.     

Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.     

ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER

A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts ： （ 1 ） computation of the velocity flow field and water surface elevation, and （2） computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.     

High accuracy eigensolution and its extrapolation for potential equations

From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations （BIEs） with the logarithmic singularity. In this paper, mechanical quadrature methods （MQMs） are presented to obtain the eigensolutions that are used to solve Laplace＇s equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone＇s collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h3-Richardson extrapolation algorithm （EA）, the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples.     

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS

Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.     

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.     

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suit- able for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.     

Powell dynamic identification of displacement parameters of indeterminate thin-walled curve box based on FCSE theory

The FCSE controlling equation of pinned thinwalled curve box was derived and the indeterminate problem of continuous thin-walled curve box with diaphragm was solved based on flexibility theory. With Bayesian statistical theory,dynamic Bayesian error function of displacement parameters of indeterminate curve box was founded. The corresponding formulas of dynamic Bayesian expectation and variance were deduced. Combined with one-dimensional Fibonacci automatic search scheme of optimal step size,the Powell optimization theory was utilized to research the stochastic identification of displacement parameters of indeterminate thin-walled curve box. Then the identification steps were presented in detail and the corresponding calculation procedure was compiled. Through some classic examples,it is obtained that stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step size is solved by adopting Fibonacci search method. And the Powell identification of displacement parameters of indeterminate thin-walled curve box has satisfied numerical stability and convergence,which demonstrates that the presented method and the compiled procedure are correct and reliable.During parameters’ iterative processes,the Powell theory is irrelevant with the calculation of finite curve strip element(FCSE) partial differentiation,which proves high computation effciency of the studied method.     

三维裂纹体应力强度因子的计算

本文采用塌缩三棱柱形奇异单元的位移计算应力强度因子，给出了一个新的全三维外推公式，它是Ｃｈｅｎ和Ｋｕａｎｇ公式〔１３〕的全三维推广，特例证明，它的精度比Ｉｎ－ｇｒａｆｆｅａ和Ｍａｎｕ的公式〔８〕高一阶。数值计算表明，结果稳定和对单元尺寸改变不敏感     

用面力边界积分方程求解断裂力学J积分

证明面力边界积分方程被积函数的散度等于零，应用Stokes公式，对平面线弹性问题，将面力边界积分的求解转化为边界点的位移势函数的点值计算。应用边界积分方程的求解结果，推导出J积分亦可表示为边界点的积分势函数的点值计算，无需进行数值积分，实例计算说明该方法的有效性。     

边界积分方程法在动态断裂力学中的数值计算研究

本文将D.Nardini和C.A.Brebbia所提出的一种动态边界积分方程新解法应用于动态断裂力学数值计算，对数值实现问题，尤其对数值稳定性及精度问题进行了详细研究，得到了能保证数值稳定性的数值解法，给出了动态断裂力学计算实例，同己有的数值结果比较，表明本文的计算是成功的。     

A numerical method for the calculation of the stokes constants

A numerical method is introduced for the computation of the Stokes constants of certain linear differential equations. The method is tested on Whittaker's equation whose Stokes constants are known analytically. The factors which affect the accuracy of the results are shown. Some numerical results for an equation similar to Whittaker's equation are presented.     

AN EFFICIENT DYNAMIC MODELING METHOD OF AN AXIALLY MOVING CANTILEVER BEAM AND FREQUENCY RESPONSE ANALYSIS

轴向移动梁动力学问题具有广泛的工程应用背景,如：机械手、机床主轴、武器身管等.计算轴向移动梁动力学响应是评估结构动力学性能以及最终指导结构设计的一个重要手段.采用Rayleigh-Ritz法、拉格朗日方程推导了轴向移动悬臂梁时变动力学方程.选取幂级数函数构造试函数对轴向移动系统动力问题进行求解.幂级数函数良好的积分与微分性能,使得推导容易以矩阵的形式快速进行,便于符号运算软件直接生成MATLAB程序.由于MATLAB基本数据单位为矩阵,符号软件生成的程序只需经过简单修改便可进行动力学计算.大大缩短了轴向移动梁从建模到动力学分析的时间,过程十分高效.通过四组算例,将本文方法计算得到的动力学响应与文献数据进行对比,对该方法准确性进行了验证,并给出了幂级数函数拟合阶数的选取原则.以此为基础,研究了轴向移动梁的频率响应特性.分为考虑重力与忽略重力两种情况,讨论了轴向振动幅度对其频率响应特性的影响.     

精细积分的非线性动力学积分方程及其解法

给出了非线性动力学积分方程的表达式,针对该方程提出了一个显式预测－校正的单步四阶精度的积分算法,适用于多自由度、强非线性,非保守系统。算例表明该方法精度高、计算量较少。     

Differential transform method for solving Richards’ equation

An approximate solution to Richards’ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method (DTM) with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.     

结构非线性动力方程的精细积分算法

基于线性方程精细积分的思路,对具有惯性、阻尼、刚度非线性的动力方程及参变非线性动力方程提出了一种较高精度线性化精细积分迭代计算算法,算例表明该算法可用较大的步长取得满意的计算精度,并可在较大的线性化区间获得较高的计算精度。     

A Computational Method for Interval Mixed Variable Energy Matrices in Precise Integration

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有限尺寸多钉连接件钉传载荷计算的解析方法

提供一种确定多钉连接件中钉传载荷的解析方法，这个方法将被连接件看作弹性体，以经典结构力学以及弹性理论平面问题复变函数解法为基础，建立了求解钉传载荷的线性代数方程组并给出了若干算例。这个方法不仅具有合理的力学模型，而且具有计算的简捷性与适用的广泛性。