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。     

复杂梁动力问题的近似分析方法

本文介绍了在各种复杂条件下，分析梁振动特性的一个近似方法－模态摄动法。这一方法是在等截面均匀梁的模态子空间内实施，将复杂梁的变系数微分方程的求解转化为代数方程组的求解。通过算例，表明这一方法简单实用，且有良好的近似性。     

广义协调元在薄壳自由振动分析中的应用

本文采用２０个自由度的矩形平板型壳单元分析薄筒壳自由振动问题。在文献（１）的基础上，将广义协调元的应用范围扩大到了壳体分析中，目的是找出简单实用的方法分析板壳这类具有特殊性质的结构。该单元由平面应力单元和平板弯曲单元经简单叠加而成，是一种性能良好的单元。沿用常规作法非常便利，程序容易实现。经算例验证，该单元自由度少，精度较好，实用方便，适合于工程应用。     

应用平板壳单元DKQl6分析板壳结构的几何非线性

应用新近开发的四边形十六自由度离Kirchhoff平板壳单元DKQl6，分析了板壳结构的几何非线性问题，采用Total Lagrange格式，在小应交、中等转动的假定下，建立了该单元几何刚度阵和大位移矩阵．非线性方程采用位移引导或弧长引导的牛顿-拉夫森增量迭代法求解．讨论了网格和加载步效对收敛性的影响，通过对典型算例的计算以及与其它单元的比较，说明了DKQl6单元在板壳结构几何非线性分析中也有良好的精度．     

车-桥系统耦合振动响应的简便计算

依据振动理论推导出了二自由度模型车辆与桥梁系统竖向耦合振动微分方程，采用模态分析的离散化方法，将复杂的偏微分方程问题转化为变系数常微分方程问题，并将微分方程数值积分的Runge-Kutta方法引入到该时变系统的振动响应计算中，使复杂的耦合响应问题得到简便的解决。通过算例验证了该方法的有效性和简便性。该方法只需要直接数值积分，具有公式简单，编程方便，计算速度快等优点，特别适合于工程实际问题的计算，并且不仅适用于匀速运动车辆，也适用于变速运动车辆。     

锥壳固有振动的精确解

本文从锥壳的Mushtari-Donnell型位移微分方程组出发,通过引入一个位移函数U(s,θ,τ)(在极限情况下,它将退化成对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程。这个方程的解用级数形式给出。     

基于拟应变法的壳单元大变形分析及在冲击动力问题中的应用

为了简便有效地解决板壳结构的大变形问题，本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成，不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法，对应变场另行假设，能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式，构造了大变形情况下的拟应变场表达式，给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明，本文针对相对自由度壳单元提出的方法及推导的公式，能够解决冲击动力问题中的大变形问题。     

板锥网壳结构的连续化分析

板锥网壳结构是一种受力性能合理，技术经济效益良好的新型空间结构形式。本文将板锥网壳结构连续化为能共同作用的特殊形式的三层薄壳，按薄壳理论建立其位移法和混合法的基本微分方程。通过对微分方程的求解，计算其整体位移及结构内力。该法具有一定的精度，可宏观地了解结构的力学性能，并可用于板锥网壳结构的初步设计。     

压电压磁圆柱壳的自由振动分析

本文基于三维弹性理论,结合状态空间理论和离散奇异卷积算法分析了压电压磁圆柱壳的自由振动问题．圆柱壳的厚度方向被作为状态空间理论的传递方向,同时应用离散奇异卷积算法对面内域进行离散．因此,初始的偏微分运动方程被转化为由一阶常微分方程构成的状态方程．离散奇异卷积算法的引入使得本方法可以处理不同边界条件,从而扩展了常规状态空间方法的应用范围．本文对数值算例的计算验证了此方法的有效性和精确度．     

球面各向同性弹性力学的位移解法

本文引入三个位移函数（ｗ，Ｇ，ψ），将球面各向同性弹性力学运动方程，简化为关于ψ的二阶偏微分方程，和关于Ｗ和Ｇ的联立方程。在静力学问题中，联立方程可进一步简化，ｗ和Ｇ可用另一位移函数Ｆ表示，而Ｆ满足一个四阶偏微分方程。在球壳固有振动问题中，则简化为一个独立的二阶常微分方程，和另两个二阶的联立的常微分方程，证明了在多层球壳中，它们分别对应独立的两类振动。改进了常微分方程的解法，并计算了一个二层球壳的频率。     

The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

We develop the Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential equations of the first order is analyzed, and tensor fields of special structure are constructed for defining characteristic vector fields naturally related with nonlinear partial differential equations of higher orders. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 26–36, January–March, 2007.     

一类偏微分方程的Hamilton正则表示

主要给出一系列关于力学中的偏微分方程的无穷维Ｈａｍｉｌｔｏｎ正则表示．其中包括变系数线性偏微分方程,ＫｄＶ方程,ＭＫｄＶ方程,ＫＰ方程,Ｂｏｕｓｉｎｅｓｑ方程等的无穷维Ｈａｍｉｌｔｏｎ正则表示．     

A moving grid method applied to one-dimensional non-stationary flame propagation

The paper presents applications of a moving grid method to the combined problem of ignition and premixed flame propagation in a closed vessel. This method belongs to the general class of adaptive grid techniques for the numerical integration of evolutionary partial differential equations and is based on the method of lines with variable node position. In the present case the motion of the grid and the solution of the partial differential equations are strongly coupled by an implicit formulation. The problem is reduced to an initial value problem for a stiff differential-algebraic system. The continuously moving grid is determined by the equidistribution of a positive function which depends on the solution of the partial differential equations. A differential-algebraic system solver is used for the time integration of the initial value problem. The numerical results of the test problems demonstrate the computational efficiency and the capability of the method to resolve the main features of the solution.     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

Multi-symplectic method for generalized Boussinesq equation

The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.     

Lie-group method of solution for steady two-dimensional boundary-layer stagnation-point flow towards a heated stretching sheet placed in a porous medium

The boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which the given partial differential equations are invariant. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the system. The effect of the velocity parameter λ, which is the ratio of the external free stream velocity to the stretching surface velocity, permeability parameter of the porous medium k ₁, and Prandtl number Pr on the horizontal and transverse velocities, temperature profiles, surface heat flux and the wall shear stress, has been studied.     

A variational analytical approach to time dependent flow of oldroyd B fluid in circular tube

In the present investigation the time dependent flow of an Oldroyd fluid B in a horizontal cylindrical pipe is stuided by the variational analytical approach developed by author. The time dependent problem is mathematically reduced to a partial differential equation of third order. Using the improved variational approach due to Kantorovich the partial differential equation can be reduced to a system of ordinary differential equations for different approximations. The ordinary differential equations are solved by the method of the Laplace transform which is led to an analytical form of the solutions. Project supported by TWAS and Chinese Academy of Sciences and the National Science Foundation of China     

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.     

微分求积单元法在结构工程中的应用

微分求积法（Differential Quadrature Method）是求鳃偏微分方程和积分-微分方程的一种数值方法,该法具有计算简便、精度较高和易于实现等优点。微分求积单元法（Differential Quadrature Element Method）是在微分求积法的基础上结合区域分割和集成规则而形成的一种新的数值计算方法,能通过自适应地选取微分求积网点数目正确模拟构件的刚度和荷载性质,其精度可通过细分单元或增加离散点数目加以提高。微分求积单元法是一种可供选择的、性能优越的数值计算方法。本文将详细论述这一数值方法的基本原理,并通过数值算例说明该方法的应用过程及其优越性,为这一方法在结构工程中的推广应用提供参考。     

Lie Algebraic Control for the Stabilization of Nonlinear Multibody System Dynamics Simulation

It is well known that when equations of motion are formulated using Lagrange multipliers for multibody dynamic systems, one obtains a redundant set of differential algebraic equations. Numerical integration of these equations can lead to numerical difficulties associated with constraint violation drift. One approach that has been explored to alleviate this difficulty has been contraint stabilization methods. In this paper, a family of stabilization methods are considered as partial feedback linearizing controllers. Several stabilization methods including the range space method, null space method, Baumgarte's method, and the damping and stiffness penalty methods are examined. Each can be construed as a particular partial feedback linearizing controller. The paper closes by comparing several of these constraint stabilization methods to another method suggested by construction: the variable structure sliding (VSS) control. The VSS method is found to be the most efficient, stable, and robust in the presence of singularities.