大型圆形贮液池力学分析中的重心插值拟谱法

针对传统大型圆形贮液池力学分析方法计算复杂、精度不高的问题,用拟谱法对圆形贮液池的线弹性静力问题进行了研究.采用重心Lagrange插值多项式建立未知函数的微分矩阵,将池壁的控制方程表示为代数方程组.通过求解代数方程组,求得池壁各个离散点挠度,进而采用微分矩阵直接求得池壁内力.算例表明,该方法原理简单,易于程序实现和数值计算精度高.     

不规则区域平面弹性问题的正则区域重心插值配点法

将不规则区域嵌入到规则的矩形区域,在矩形区域上将弹性平面问题的控制方程采用重心Lagrange插值离散,得到控制方程矩阵形式的离散表达式。在边界节点上利用重心插值离散边界条件,规则区域采用置换法施加边界条件,不规则区域采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法进行求解,得到整个规则区域上的位移数值解。利用重心插值计算得到不规则区域内任意节点的位移值,计算精度可到10^-14以上。数值算例验证了所建立方法的有效性和计算精度。     

弹性理论中的临界变分及消除方法

临界变分现象是拉氏乘子法的固有特性，钱伟长应用高阶拉氏乘子消除了临界变分现象。本文将提出一种新的方法－凑合反推法，这种方法摒充了拉氏乘子法，把拉氏乘子所在的项目一个待定函数Ｆ代替。这样构成的泛函，作者称之为试泛函。而待定函数Ｆ的识别类似于拉氏乘子的识别。通过该法可以方便地构造出各种多变量广义变分原理，并且可以消除临界变分现象。     

A mixture differential quadrature method for solving two-dimensional incompressible Navier-Stokes equations

Ｔｈｅｄｉｆｆｅｒｅｎｔｉａｌｑｕａｄｒａｔｕｒｅｍｅｔｈｏｄ（ＤＱＭ）ｐｒｏｐｏｓｅｄｂｙＲ．Ｂｅｌｌｍａｎ［１,２］ｈａｓｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙｅｍｐｌｏｙｅｄｉｎｎｕｍｅｒｉｃａｌｃｏｍｐｕｔａｔｉｏｎｓｏｆｐｒｏｂｌｅｍｓｉｎｅｎｇｉｎｅｅｒｉｎｇａｎｄｐｈｙｓｉｃａｌｓｃｉｅｎｃｅ．ＢｅｃａｕｓｅｔｈｅｉｎｆｏｒｍａｔｉｏｎｏｎａｌｌｇｒｉｄｐｏｉｎｔｓｉｓｕｓｅｄｔｏｆｉｔｔｈｅｄｅｒｉｖａｔｉｖｅｓａｔｇｒｉｄｐｏｉｎｔｓｉｎｔｈｅＤＱＭ,ｉｔｉｓｅｎｏｕｇｈｔｏｏｂｔａ…     

Flexible shaft whirl induced by dry friction and its stability

This paper is devoted to the study of the whirling phenomena of flexible rotors due to dry friction. The mechanical model used here is a two-degree-of-freedom system in which the rubbing plane is not coincident with the rotating plane of the lumped mass. The characteristic equation of whirl speeds is derived and the whirling modes are obtained. The dynamic stability of each admissible whirling motion is also discussed. The results show that the whirl speeds are always higher than the critical speed of the shaft.     

基于Uzawa算法的弹塑性扭转问题的局部微分求积法

研究了由椭圆变分不等式描述的弹塑性扭转问题,构造了基于Uzawa算法的局部微分求积法,给出了数值算例,通过与有限元方法的比较,说明了方法的有效性。     

The Variational Principle and Application of Numerical Manifold Method

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＮｕｍｅｒｉｃａｌＭａｎｉｆｏｌｄＭｅｔｈｏｄ(ＮＭＭ )ｉｓａｎｅｗｎｕｍｅｒｉｃａｌａｎａｌｙｓｉｓｍｅｔｈｏｄ ,ｗｈｉｃｈｉｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆｆｉｎｉｔｅｃｏｖｅｒｔｅｃｈｎｏｌｏｇｙｉｎｍａｎｉｆｏｌｄａｎａｌｙｓｉｓ.ＩｔｄｉｆｆｅｒｓｆｒｏｍＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｉｎｔｈａｔｔｈｅｆｉｎｉｔｅｃｏｖｅｒｓｏｆＮＭＭａｒｅｃｏｎｓｉｓｔｉｎｇｏｆｍａｔｈｅｍａｔｉｃａｌｃｏｖｅｒｓａｎｄｐｈｙｓｉｃａｌｃｏｖｅｒｓａｎ…     

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

ＦｕＢａｏｌｉａｎ（付宝连）（ＲｅｃｅｉｖｅｄＮｏｖ．２２，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩ...     

An analysis and calculation on unsteady flow in exhaust system of diesel engine

In this paper, the unsteady and non-homoentropic flow in exhaust system of diesel engine is analysed and calculated by means of characteristic method. This paper makes proper treatment in calculation, particularly in calculation of boundary conditions, then the calculation program obtained is rather common and the convergence of calculation is faster too. Finally, in this paper, we take exhaust system of 6135 turbocharged diesel engine for an example and make numerical calculation for it, The results obtained are quite satisfactory.     

初始几何缺陷的功能梯度梁振动特性分析

对于初始几何缺陷的功能梯度梁的振动问题,基于功能梯度材料的细观结构模型,采用幂函数模拟材料组分沿梁厚度方向的变化规律;基于Euler–Bernoulli梁理论,从几何方程和Marguerre应变得到了轴向应变的表达式,利用Hamilton原理推导了初始几何缺陷的功能梯度梁的运动微分方程,并进行无量纲化;运用微分求积法对无量纲振型微分方程以及边界条件进行离散,得到了特征方程;最后,分析了初始几何缺陷的功能梯度梁的梯度指标、初始的几何曲率、边界约束对其无量纲固有频率和振型的影响。

     

热载荷下粘弹性功能梯度材料薄板的准静态响应

由热粘弹性功能梯度材料的本构方程出发,利用Laplace变换,通过引进薄板的"结构函数"和"热函数",建立了各向同性薄板的数学模型.采用卷积双线性形式,给出了薄板准静态问题的简化Gurtin型泛函.在空域上和时域上分别采用Ritz法和Legendre插值法考察了温度变化和功能梯度对于薄板响应的影响.     

混凝土中爆炸数值仿真算法研究

用AUTODYN动力学软件对装药在混凝土介质靶中爆炸作数值仿真,研究了不同的网格描述方法,以及网格划分方法对计算结果的影响。通过实际算例比较了Lagrange算法和SPH算法以及不同的网格划分细度对靶径向、轴向不同距离的最大冲击压力、靶背过载以及损伤区、炸坑大小的模拟计算结果。分析得到了混凝土介质靶中爆炸问题数值仿真的合适算法,即拉氏算法对炸点近处的较高的最大冲击压力有较好的敏感能力,SPH算法对仿真计算爆坑形态以及抛掷体速度等具有明显的优势。对于算例问题,拉氏算法10 mm网格和SPH算法3 mm粒子即可满足一定的计算精度。     

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.     

Galerkin meshless methods based on partition of unity quadrature

Introduction Meshlessmethodsarenewmethodsofnumericalcomputationwhichhavebeendeveloped rapidlyinrecentyears.Inthesemethods,onlynodesareneeded,meshinformationistotally unnecessary.Thiscanavoidorpartlyavoidthedifficultyofmeshgeneration.Duetohigh accuracyandstability,Galerkinmeshlessmethodsareappliedbroadly,butitisunavoidable tocomputetheintegrationoverthewholephysicaldomaininGalerkinweakform,whichisa greatchallengeforGalerkinmeshlessmethodsbecauseoftheabsenceofmesh.TocarryouttheintegrationinGal…     

基于微分求积法的边界值方法

探究了边界值方法与微分求积法两者之间的关系。利用经典的微分求积公式,系统地构造了三类不同的边界值方法;当采用均匀网格点时,本文所导出的边界值方法与已有的边界值方法是一致的。研究结果揭示了微分求积法与边界值方法两者之间的内在关系,也建立了线性多步法与单步多级方法之间的联系。     

A high‐order triangular discontinuous Galerkin oceanic shallow water model

A high‐order triangular discontinuous Galerkin (DG) method is applied to the two‐dimensional oceanic shallow water equations. The DG method can be characterized as the fusion of finite elements with finite volumes. This DG formulation uses high‐order Lagrange polynomials on the triangle using nodal sets up to 15th order. Both the area and boundary integrals are evaluated using order 2N Gauss cubature rules. The use of exact integration for the area integrals leads naturally to a full mass matrix; however, by using straight‐edged triangles we eliminate the mass matrix completely from the discrete equations. Besides obviating the need for a mass matrix, triangular elements offer other obvious advantages in the construction of oceanic shallow water models, specifically the ability to use unstructured grids in order to better represent the continental coastlines for use in tsunami modeling. In this paper, we focus primarily on testing the discrete spatial operators by using six test cases—three of which have analytic solutions. The three tests having analytic solutions show that the high‐order triangular DG method exhibits exponential convergence. Furthermore, comparisons with a spectral element model show that the DG model is superior for all polynomial orders and test cases considered. Copyright © 2007 John Wiley & Sons, Ltd.     

数值流形方法的粘性边界问题初探

在实际工程数值流形方法分析中,采用固定约束边界的方法处理无限域或者半无限域的情况,边界处应力波的反射造成模拟结果与实际情况不符.本文基于Lysmer等人提出的粘性边界理论,在边界上设置阻尼器,推导相应粘性边界条件下流形单元刚度矩阵的数值计算格式,经岩石长条中弹性波传播算例,并与有限元结果对比,验证了该粘性边界的有效性,有利于数值流形方法的工程中推广应用.     

有限谱ENO格式及其应用

首先对王健平提出的有限谱法^[1-3]做了进一步的理论研究，发现了一些新的有限谱法的插值基函数组，并互将有限谱法应用在ENO格式中，构造了有限谱ENO计算格式，然后通过对一维Euler方程的几个经典的模型问题和二维湍流与弱激波相互作用问题的数值计算，并且与理论解或准精确解进行比较分析，从而表明了此格式对于激波和其他间断具有较高的分辨率，在激波附近基本上没有明显的数值振荡，而且对于流场中的细致结构也具有相当高的精度。