结构动力方程的增维精细积分法

对线性定常结构动力系统提出的精细积分方法,能够得到在数值上逼近于精确解的结果,但对于非齐次动力方程涉及到矩阵求逆的困难。提出采用增维的办法,将非齐次动力方程转化为齐次动力方程,在实施精细积分过程中不必进行矩阵求逆,这种方法对于程序实现和提高数值稳定性十分有利,而且在大型问题中计算效率较高,从而改进了精细积分方法的应用,数值例题显示了本文方法的有效性。     

非线性动力方程精细积分法的自适应步长研究

基于Adams显式和隐式预估公式实现对时间步长的 自适应选择,利用当前时刻v(tk),采用预估公式的两种形式(显式与隐式),对v(tk+1)进行两次预估,利用两公式局部截断误差关系,得出误差估计值ξ(tk+1),并根据其大小 自适应调节时间步长.将该思想应用于预估型(求解过程需要用到预估公式)精细积分算法中,使精细积分...     

非线性动力方程的三次样条-增维精细算法

提出一种针对非线性动力方程的改进精细积分方法。该方法是在时间步长内采用分段的三次样条函数拟合非齐次项,保持高精度拟合的同时避免了求导运算和高次多项式插值带来的Runge现象。通过引入4×2个变量将动力方程增加四维转化为齐次方程,并建立相应的通解格式,避免了状态空间下系统矩阵求逆。将指数矩阵分为四个子模块,利用各模块的特点分别进行理论推导及基于精细积分法进行分步、分块计算得到相应的理论解和高精度数值解,无需反复计算整个指数矩阵,提高了解算效率。针对含未知状态量的非齐次项,引入预测-校正的方法进行迭代求解。数值计算结果表明了本文方法的有效性。     

增维精细积分法的适用范围研究

对线性定常结构动力系统提出的增维精细积分法,能够将非齐次动力方程转化为齐次动力方程,不用对状态矩阵求逆就能方便高效地求解出结构的动力响应。本文在仔细分析增维精细积分法性质的基础上,提出了其适用条件,进一步拓宽了其应用范围,并给出了将荷载项展开成傅里叶级数时,相应增维精细积分法的表达式。同时,在一个时间步长内,通过对非齐次项作线性化假设,成功地将增维精细积分法应用到了非线性动力分析领域。本文方法计算格式统一,易于编程,具有很高的计算效率。数值算例证明了本文方法的有效性。     

二维扩散方程的单点子域精细积分法

建立了二维扩散方程的单点子域精细积分法,并通过稳定性分析,表明了单点子域精细积分法相对于差分法的优越性。     

矩阵黎卡提方程的精细积分法

选择恰当的参数,将２￣Ｎ类算法用于代数与微分黎卡提方程。证明了算得的解是如此精确,几乎是计算机上的精确解。数例验证了该结论。     

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.     

矩阵黎卡提方程的精细积分法

选择恰当的参数，将２＾Ｎ类算法用于代数与微分黎卡提方程。证明了算得的解是如此精确，几乎是计算机上的精确解。数例验证了该结论。     

非线性结构动力方程的自适应步长数值算法

基于Runge-Kutta法实现对时间步长的 自适应选择,研究提高非线性结构动力方程的计算精度.利用Runge-Kutta公式的局部截断误差,得出误差估计值ζn+1,根据ζn+1的大小 自适应调节时间步长的大小,为算法提供一个判断语句,其能使算法流程图更加多样性.将该思想应用于经典Runge-Kutta算法和精细Runge-Kutta算法中,得到自适应步长的经典Runge-Kutta算法和精细Runge-Kutta算法,使算法的时间步长依赖于给定的每步误差限值,提高计算精度,数值算例论证了本文方法的有效性.     

一类非线性周期系统响应的精细积分法

对于一类非线性周期／变系数微分方程,提出基于精细积分法的数值解法,处理非线性周期／变系数微分方程系统的响应问题,其积分策略是：采用精细积分格式处理常系数部分;采用线性插值格式处理非线性周期／变系数部分,既继承精细积分方程高度准确的特点,又保证足够的精度与较小的计算量。通过数值算例,与以往与用的微分方程直接数值积分法（如预估－校正哈明法）求得的解加以比较表明,对于给定的精度要求,精细积分法更经济有效     

TIME PRECISE INTEGRATION METHOD FOR CONSTRAINED NONLINEAR CONTROL SYSTEM

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｓｔａｂｌｉｓｈｍｅｎｔｏｆｔｈｅｔｉｍｅｐｒｅｃｉｓｅｉｎｔｅｇｒａｔｉｏｎｍｅｔｈｏｄｐｒｏｖｉｄｅｓａｎｅｗｗａｙｆｏｒｔｈｅｃｏｍｐｕｔａｔｉｏｎｏｆｄｙｎａｍｉｃｓｙｓｔｅｍｓ[1].Ｔｈｅａｂｏｖｅｍｅｔｈｏｄ ,ｂａｓｅｄｏｎｔｈｅｓｉｍｕｌａｔｉｏｎｒｅｌａｔｉｏｎｂｅｔｗｅｅｎｃｏｍｐｕｔａｔｉｏｎａｌｓｔｒｕｃｔｕｒａｌｍｅｃｈａｎｉｃｓａｎｄｏｐｔｉｍａｌｃｏｎｔｒｏｌ,ｗａｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆｔｈｅｓｕｂｓｔｒｕｃｔｕｒａ…     

ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

IntroductionThepreciseintegrationmethod(PIM) [1],whichwasproposedforsolvingstructuraldynamicequations.Thismethodissimplerandpossesseshigherprecision .Forlinearsteadystructuraldynamicsystems,itsnumericalresultsattheintegrationpointsarealmostequaltothatoftheexactsolutioninmachineaccuracy .InthepreciseintegrationmethodforsolvingPDEs,theequationsshouldbediscretizedinthephysicalspaceforobtainingthesystemofODEsintime ,whichisoftenexecutedbythefinitedifferencemethodorthefiniteelementmethod .Inrec…     

An improved precise integration method for nonlinear dynamic system

In the present paper, based on the precise integration method established in linear dynamic system, an improved precise integration method is presented for nonlinear dynamic system. Firstly, the nonlinear dynamic system is converted into an augmented Lie type dynamic system. Then the precise integration method is improved for solving the above augmented equation and preserving its group structure in the meantime. Finally, two numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.     

Characteristic Galerkin method for convection-diffusion equations and implicit algorithm using precise integration

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability. The project sponsored by the State Scientific and Technological Commission of China through “China State Key Project: the Theory and Methodology for Scientific and Engineering Computations with Large Scale”, the National Natural Science Foundation of China and the European Commission Research Project CI1^*CT94-0014.     

计算结构动力响应的分段精细时程积分方法

利用钟万勰等发展的精细时程积分方法,提出了解线性定常结构动力系统响应的分段精细进程积分方法,它能适用于各种激励作用下系统的动力响应。对于载荷项采用线性和两次多项式进行拟合,采用精细时程积分方法和叠代方法对动力响应进行计算,与传统的离散积分方法如纽马克方法和威尔逊方法等及状态方程直接积分方法进行数值比较,本方法具有很高的精度和计算效率。     

层合圆柱三维温度场分析的半解析-精细积分法

针对圆柱体的三维温度场分析,提出了一种高效的半解析-精细积分法。将温度场展开为环向坐标的Fourier级数,并对径向坐标进行差分离散,从而把三维热传导方程简化为一系列二阶常微分方程;将这些二阶常微分方程转化为哈密顿体系下的一阶状态方程,并利用两点边值问题的精细积分法求解。由于该方法仅对径向坐标进行差分离散,故相对于传统的数值方法离散规模大幅度减少,不仅提高了计算效率、降低了存贮量,而且缓解了代数方程的病态问题。此外,针对Fourier半解析解,根据热平衡原理推导出了两种材料衔接面的半解析差分方程,从而为求解复合材料层合柱问题打下了基础。算例结果表明,即使对于细长比高达400的圆柱杆件,此方法仍然可以给出精度较高的解答。     

基于Householder方法的子域精细积分

有限元法生成的矩阵通常具有尺度和带宽很大的特点,应用子域精细积分面临着选择子域的困难。本文采用Householder方法将矩阵三对角化,从而使子域精细积分可用于大型有限元系统。通过在子域精细积分中引入预估-校正格式,可以在不需要迭代的情况下得到比蛙跳格式更高的精度。     

An adaptive algorithm of precise integration for transient analysis

This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems. The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method, can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method. Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

Remarks on nonlinear Galerkin method for Kuramoto-Sivashinsky equation

I.TheEquation-ConsidertheKuramoto-Sivashinskyequati0nwithperiodicboundaryconditiontwherev>Oisarbitraryandu,(x)isl-peri0dicandofzeromean.ThisequationcanberewrittenasanabstractevolutionequationinaHilbertspeceHendowedwithascalarproduct',')andanorml'I.Here,we…     

A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (19872016, 50178016, 19832010) and the Foundation for University Key Teacher by the Ministry of Education of China