求解平面和轴对称热冲击问题的热权函数有限元法

根据三维通用权函数法的普遍表达式,给出了轴对称问题和平面问题热权函数法的基本公式,并利用刚度阵导数法,将热权函数法与有限元法直接耦合,给出了二维问题的热权函数有限元法计算格式,实例计算表明,该文给出的计算方法具有极高的计算效率和满意的工程应用精度。     

用间断分解法解一维应力波波动问题

间断分解法在计算气体动力学和计算水力学方面已经有了成功的应用，这个方法的核心是求解守恒型方程的Ｒｉｅｍａｎｎ问题，即进行初始间断的分解计算。本文将这种方法推广应用于一维应力波的计算，给出了计算的原理和算法，并得到较好结果。     

空间刚架结构的广义逆力法

在结构计算中，根据算法中所采用的基本未知量的不同．结构分析方法可以分为力法、位移法和混合法。其中位移法由于适宜计算机处理而在结构计算领域得到了广泛的应用．经典力法相比之下应用就远不如位移法普遍，虽然力法本身在力学上有其独特的优势。广义逆矩阵做为一种较新的数学工具，自二十世纪五十年代诞生以来正日益表现出越来越旺盛的生命力。广义逆力法就是一种基于力法和广义逆矩阵理论的新的迭代算法。这种算法是一种完全适合计算机处理的力法方法。该算法的思路以及对于求解线弹性空间刚架结构问题的具体公式均在文中给出并给出了算例。从算例计算结果可以看到广义逆力法有着较好的计算效率和计算精度。该算法的提出为力法在计算机计算领域的应用开拓了新的发展空间。该算法在材料非线性问题和结构并行计算方面也有着较好的应用前景。     

拉压双模量问题的动力分析

给出拉压双模量单自由度振支解析解，应用逐步积法，求解拉压双模量多自由度振动问题，计算分析显示此类材料的一些振动特性和特殊现象。     

任意支承条件下连续板系结构的有限板块解法

本文基于薄板小挠度弯曲理论，构造出板元内部解析，边界挠度和边界法向弯矩以带补充项的付氏级数逼近，同时考虑域内多点支承作用的板元位移函数，给出了一处适用于任意支承条件下连续板系结构的有限板块法求解格式。数值计算结果表明：本文的方法具有良好的计算精度和计算效率，适于工程应用。     

板自由振动问题的域外奇点解法

本文应用域外奇点法求解板的自由振动问题，给出了各种边界条件的表达式，计算了固支正方形板的固有频率，得到满意的结果．     

二维正态分布函数值的一个近似算法

二维正态分布函数值的计算是估算串联结构体系失效概率上、下限的一项重要内容。目前一般常采用两种方法，即数值积分和界限法。前者因计算量大，耗时多不便实用，后者使结构体系失效率的上、下界限进一步变宽。本文给出一个计算二维正态分布函数值的近似方法。实际计算表明，本方法计算效率高，精度完全能满足工程应用要求     

结构可靠度分析的响应面法及其Matlab实现

对功能函数不能明确表达的问题进行可靠度分析，常采用响应面法。其中以求得验算点为目的迭代的二次多项式序列响应面法应用较为广泛，本文给出了该方法的Mattab源程序。提出了基于Mattab的插值响应面法和BP神经网络响应面法，介绍了其在Mattab环境下的实现方法，并进行了三种方法的对比分析。Mattab语言基本元素是矩阵，提供了各种矩阵的运算和操作，其中包含结构可靠度计算中常用的各种数值计算方法工具箱。采用Mattab语言构造响应面函数，进行结构可靠度计算，可充分发挥其矩阵运算功能及各种工具箱的作用，使编程效率大大提高，且语法简便，易于掌握。Mattab语言在可靠度计算中的应用，会对结构可靠性理论的推广使用起到积极推进作用。     

工程系统可靠度的逻辑分析与优化设计

基于结构逻辑图的理论，提出了以下确界算子和上确界算子分别作为串联与并联系统可靠度的计算模型；形成了复杂工程系统可靠度的逻辑分析方法。在此基础上，应用多阶段决策算子法，成功地求解了工程系统可靠度的优化设计问题；给出了桁架结构优化的数值计算例题。     

火炮多体动力学相似模型分析

本文给出了火炮发射运动的多刚体系统动力学模型，运用拉格朗日方法建立了动力学方程；应用相似理论建立了原型和模型的动力相似关系，通过数值计算、实弹试验验证了相似模型的正确性     

热传导问题灵敏度分析的伴随法

在热传导灵敏度分析的直接法的研究基础上，进一步探讨了稳态和瞬态热传导问题灵敏度分析的伴随法.推导了伴随法的计算列式，对于瞬态热传导问题，研究了瞬态约束处理的关键点方法，并提出伴随方程的精细积分解法。算例表明，稳态问题灵敏度计算，伴随法与直接法的结果是一致的；瞬态问题灵敏度计算，两种方法的精度相当。     

THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

IntroductionNumerical manifold method is a new numerical method established on the basis of finitecover of manifold[1,2].By using continuous and non-continuous finite cover system,thenumerical manifold method includes the continuous and non-continuous as …     

一种基于半参数回归的加速度计误差模型辨识方法

为了解决加速度计离心机试验中系统误差和未建模误差对加速度计模型辨识的影响,将统计学中的半参数回归方法引入到加速度计的模型辨识中,建立了加速度计的半参数回归模型,提出了一种基于最小二乘-半参数回归模型(LS-SPRM)的估计方法,该估计方法利用最小二乘法估计加速度计的误差模型系数,利用半参数回归方法估计加速度计测试中的系统误差,并通过检验残差是否为白噪声作为判断是否有系统误差的条件。在半参数模型的估计中,采用二阶段估计方法,利用三次样条函数进行非参数部分的估计,并讨论了光滑参数的选取方法。仿真试验结果表明,采用该方法能够较好地补偿由于系统误差和未建模误差带来的影响,使加速度计模型辨识的标准差较普通最小二乘法减小45%左右,估计的残差也减小了近一倍。     

A new appraoch of the dynamic substructure method

Researches show that there exists a modal transformation matrix which is similar to that of the fixed interface method in form but slightly different from that in content. Using the constrained modes and normal modes or Lanczos vectors, a new modal transformation developed from hybrid method is given, in which the interface forces are replaced by interface displacements. The first synthesis equations are assembled easily as with the fixed interface method, yet the interface coordinates can be further eliminated as with the free-interface method. The new method unifies the fixed- and free-interface methods as well as hybrid method,permitting easy implementation of the Lanczos vectors to replace normal modes so that only static modes are calculated. The dynamic substructure method thus becomes more flexible and efficient. This reveals the interrelations of various dynamic substructure methods. New formula for modal analysis and modal synthesis are developed and three examples are given for illustration.Supported by Doctoral Training Foundation of State Education Commission and NNSF of China.     

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.     

Determination of mode shapes using wavelet transform of free vibration data

In this article, a new method is proposed to determine the mode shapes of linear dynamic systems with proportional viscous damping excited by an impact force. The time signals of responses and a priori knowledge of the natural frequencies are required in this method. The method is particularly suitable for the wavelet techniques which can precisely estimate the natural frequencies. A previously proposed method based on a modified Morlet wavelet function with an adjusting parameter is used to identify the natural frequencies and damping ratios of system, and the mode shapes are estimated using the proposed method in this work. It is shown that the extracted mode shapes are not scaled. Therefore, mass change method is used for scaling the mode shapes. Moreover, the effect of noise on the extracted modal parameters is investigated. The validity of method is demonstrated using numerical and experimental case studies.     

旋转厚壳的自由振动计算

由板壳理论及Ｍｉｎｄｌｉｎ假设，导出了旋转厚壳的一阶基本微分方程组。求解时采用了子结构离散变量法。文末给出了算例。     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

Numerical and analytical methods for in-plane dynamic response of annular disk

A new method called the moving element method is formulated to solve two problems in a unified framework: (a) rotating disk subjected to stationary load and (b) stationary disk subjected to rotating load. The method involves discretization of the disk into “moving elements”. But unlike in the conventional finite element method, these elements rotate relative to the disk and are not attached to material points. Analytical solutions in terms of complex Fourier–Hankel series are also presented. Numerical examples show good agreement between the proposed numerical method and the analytical method. The advantages of the proposed method over the analytical method and the finite element method are illustrated.     

三维车桥耦合系统的非平稳随机振动分析

推导了线性时变系统非平稳随机响应的多维虚拟激励法,研究了三维车桥耦合系统受轨道激励而产生的非平稳随机振动。桥梁模型采用空间Euler梁单元,轨道激励假设为均匀调制多点异相位非平稳随机激励。采用多维虚拟激励法把轨道不平度转化为一系列简谐不平度的叠加,通过简单分解精细积分格式进行迭代计算,最终得到系统随机响应的时变功率谱及均方根。数值算例中,用时间历程法验证了本文方法的正确性,并且分析了方向、高低、水平三类轨道激励同时作用下三维车桥耦合系统的非平稳随机振动特性。